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42 results on '"Zoran Ristivojevic"'

1. Density profile of a semi-infinite one-dimensional Bose gas and bound states of the impurity

Author

Aleksandra Petković, Benjamin Reichert, and Zoran Ristivojevic

Subjects
Physics, QC1-999
Abstract

We study the effect of the boundary on a system of weakly interacting bosons in one dimension. It strongly influences the boson density, which is completely suppressed at the boundary position. Away from it, the density is depleted over the distances on the order of the healing length at the mean-field level. Quantum fluctuations modify the density profile considerably. The local density approaches the average one as an inverse square of the distance from the boundary. We calculate an analytic expression for the density profile at arbitrary separations from the boundary. We then consider the problem of localization of a foreign quantum particle (impurity) in the potential created by the inhomogeneous boson density. At the mean-field level, we find exact results for the energy spectrum of the bound states, the corresponding wave functions, and the condition for interaction-induced localization. The quantum contribution to the boson density gives rise to small corrections of the bound-state energy levels. However, it is fundamentally important for the existence of a long-range Casimir-like interaction between the impurity and the boundary.

Published
2020
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2. Damping of elementary excitations in one-dimensional dipolar Bose gases

Author

Hadrien Kurkjian and Zoran Ristivojevic

Subjects
Physics, QC1-999
Abstract

In the presence of dipolar interactions, the excitation spectrum of a Bose gas can acquire a local minimum. The corresponding quasiparticles are known as rotons. They are gapped and do not decay at zero temperature. Here we study the decay of rotons in one-dimensional Bose gases at low temperatures. It predominantly occurs due to the backscattering of thermal phonons on rotons. The resulting rate scales with the third power of temperature and is inversely proportional to the sixth power of the roton gap near the solidification phase transition. The hydrodynamic approach used here enables us to find the decay rate for quasiparticles at practically any momenta, with minimal assumptions on the exact form of the interparticle interactions. Our results are an essential prerequisite for the description of all the dissipative phenomena in dipolar gases and have direct experimental relevance.

Published
2020
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3. Analytical results for the capacitance of a circular plate capacitor

Author

Benjamin Reichert and Zoran Ristivojevic

Subjects
Physics, QC1-999
Abstract

We study the classic problem of the capacitance of a circular parallel plate capacitor. At small separations between the plates, it was initially considered in the 19th century by Kirchhoff, who found the leading and the subleading term in the capacitance. Despite a large interest in the problem, almost 150 years later, only the second subleading term has been found analytically. Using the recent advances in the asymptotic analysis of Fredholm integral equations of the second kind with finite support, here we study the one governing the circular capacitor, known as the Love equation. We find analytically many subleading terms in the capacitance at small separations. We also calculate the asymptotic expansion at large separations, thus providing two simple expressions which practically describe the capacitance at all distances. The approach described here could be used to find exact analytical expansions for the capacitance to an arbitrary number of terms in regimes of both small and large separations.

Published
2020
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4. The Casimir-like effect in a one-dimensional Bose gas

Author

Benjamin Reichert, Zoran Ristivojevic, and Aleksandra Petković

Subjects
Casimir-like interaction, Bose system, one-dimensional quantum system, Science, Physics, QC1-999
Abstract

The electromagnetic Casimir effect manifests as the interaction between uncharged conducting objects that are placed in a vacuum. More generally, the Casimir-like effect denotes an induced interaction between external bodies in a fluctuating medium. We study the Casimir-like interaction between two impurities embedded in a weakly interacting one-dimensional Bose gas. We develop a theory based on the Gross–Pitaevskii equation that accounts for the effect of quantum fluctuations. At small separations, the induced interaction between the impurities decays exponentially with the distance. This is a classical result that can be understood using the mean-field Gross–Pitaevskii equation. We find that at larger distances, the induced interaction crosses over into a power law dependence due to the quantum fluctuations. We obtain an analytic expression for the interaction that interpolates between the two limiting behaviors. The obtained result does not require any regularization.

Published
2019
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5. Exact Results for the Moments of the Rapidity Distribution in Galilean-Invariant Integrable Models

Author

Zoran Ristivojevic, Laboratoire de Physique Théorique (LPT), Institut de Recherche sur les Systèmes Atomiques et Moléculaires Complexes (IRSAMC), Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3), and Université de Toulouse (UT)-Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Statistical Mechanics (cond-mat.stat-mech), Quantum Gases (cond-mat.quant-gas), [PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph], General Physics and Astronomy, FOS: Physical sciences, Mathematical Physics (math-ph), Condensed Matter - Quantum Gases, Condensed Matter - Statistical Mechanics, Mathematical Physics
Abstract

We study a class of Galilean-invariant one-dimensional Bethe ansatz solvable models in the thermodynamic limit. Their rapidity distribution obeys an integral equation with a difference kernel over a finite interval, which does not admit a closed-form solution. We develop a general formalism enabling one to study the moments of the rapidity distribution, showing that they satisfy a difference-differential equation. The derived equation is explicitly analyzed in the case of the Lieb-Liniger model and the moments are analytically calculated. In addition, we obtained the exact information about the ground-state energy at weak repulsion. The obtained results directly enter a number of physically relevant quantities., Comment: 6 pages

Published
2022
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6. Method of difference-differential equations for some Bethe-ansatz-solvable models

Author

Zoran Ristivojevic, Laboratoire de Physique Théorique (LPT), Institut de Recherche sur les Systèmes Atomiques et Moléculaires Complexes (IRSAMC), Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3), and Université de Toulouse (UT)-Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Statistical Mechanics (cond-mat.stat-mech), [PHYS.QPHY]Physics [physics]/Quantum Physics [quant-ph], Quantum Gases (cond-mat.quant-gas), FOS: Physical sciences, Mathematical Physics (math-ph), Condensed Matter - Quantum Gases, Condensed Matter - Statistical Mechanics, Mathematical Physics
Abstract

In studies of one-dimensional Bethe ansatz solvable models, a Fredholm integral equation of the second kind with a difference kernel on a finite interval often appears. This equation does not generally admit a closed-form solution and hence its analysis is quite complicated. Here we study a family of such equations concentrating on their moments. We find exact relations between the moments in the form of difference-differential equations. The latter results significantly advance the analysis, enabling one to practically determine all the moments from the explicit knowledge of the lowest one. As applications, first we study the moments of the quasimomentum distribution in the Lieb-Liniger model and find explicit analytical results. The latter moments determine several basic quantities, e.g., the $N$-body local correlation functions. We prove the equivalence between different expressions found in the literature for the three-body local correlation functions and find an exact result for the four-body local correlation function in terms of the moments of the quasimomentum distributions. We eventually find the analytical results for the three- and four-body correlation functions in the form of asymptotic series in the regimes of weak and strong interactions. Next, we study the exact form of the low-energy spectrum of a magnon (a polaron) excitation in the two-component Bose gas described by the Yang-Gaudin model. We find its explicit form, which depends on the moments of the quasimomentum distributions of the Lieb-Liniger model. Then, we address a seemingly unrelated problem of capacitance of a circular capacitor and express the exact result for the capacitance in the parametric form. In the most interesting case of short plate separations, the parametric form has a single logarithmic term. This should be contrasted with the explicit result that has a complicated structure of logarithms., Comment: 12 pages

Published
2022

7. Quasiparticle Energy Relaxation in a Gas of One-Dimensional Fermions with Coulomb Interaction

Author

Zoran Ristivojevic, Konstantin I. Matveev, Fermions Fortement Corrélés (LPT) (FFC), Laboratoire de Physique Théorique (LPT), Institut de Recherche sur les Systèmes Atomiques et Moléculaires Complexes (IRSAMC), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche sur les Systèmes Atomiques et Moléculaires Complexes (IRSAMC), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439, USA, Argonne National Laboratory [Lemont] (ANL), Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Fédération de recherche « Matière et interactions » (FeRMI), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3), and Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Physics, Strongly Correlated Electrons (cond-mat.str-el), Condensed matter physics, FOS: Physical sciences, General Physics and Astronomy, Inverse, 02 engineering and technology, Fermion, 021001 nanoscience & nanotechnology, 01 natural sciences, 7. Clean energy, Condensed Matter - Strongly Correlated Electrons, Excited state, 0103 physical sciences, Quasiparticle, Coulomb, Relaxation (physics), [PHYS.COND.CM-SCE]Physics [physics]/Condensed Matter [cond-mat]/Strongly Correlated Electrons [cond-mat.str-el], 010306 general physics, 0210 nano-technology, Scaling, ComputingMilieux_MISCELLANEOUS, Excitation
Abstract

We consider a system of charged one-dimensional spin-$\frac{1}{2}$ fermions at low temperature. We study how the energy of a highly-excited quasiparticle (or hole) relaxes toward the chemical potential in the regime of weak interactions. The dominant relaxation processes involve collisions with two other fermions. We find a dramatic enhancement of the relaxation rate at low energies, with the rate scaling as the inverse sixth power of the excitation energy. This behavior is caused by the long-range nature of the Coulomb interaction.

Published
2021

8. Mediated interaction between polarons in a one-dimensional Bose gas

Author

Aleksandra Petkovic, Zoran Ristivojevic, Fermions Fortement Corrélés (LPT) (FFC), Laboratoire de Physique Théorique (LPT), Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Fédération de recherche « Matière et interactions » (FeRMI), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3), and Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)

Subjects
[PHYS.COND.GAS]Physics [physics]/Condensed Matter [cond-mat]/Quantum Gases [cond-mat.quant-gas], Quantum Gases (cond-mat.quant-gas), Atomic Physics (physics.atom-ph), FOS: Physical sciences, Condensed Matter - Quantum Gases, ComputingMilieux_MISCELLANEOUS, Physics - Atomic Physics
Abstract

We study a weakly-interacting one-dimensional Bose gas with two impurities coupled locally to the boson density. We derive analytical results for the induced interaction between the impurities at arbitrary coupling and separation $r$. At $r\lesssim \xi$, where $\xi$ denotes the healing length of the Bose gas, the interaction is well described by the mean-field contribution. Its form changes as the coupling is increased, approaching a linear function of $r$ at short distances in the regime of strong coupling. The mean-field contribution decays exponentially at arbitrary coupling for $r\gg\xi$. At such long distances, however, the effect of quantum fluctuations becomes important, giving rise to a long-ranged quantum contribution to the induced interaction. At longest distances it behaves as $1/r^3$, while at strong coupling we find an intermediate distance regime with a slower decay, $1/r$. The quantum contribution in the crossover regime is also calculated. The induced interaction between impurities (i.e., polarons) is attractive and leads to the formation of their bound state, known as bipolaron. We discuss its binding energy., Comment: 6 pages, 2 figures

Published
2021

9. Dispersion relation of a polaron in the Yang-Gaudin Bose gas

Author

Zoran Ristivojevic, Laboratoire de Physique Théorique (LPT), Institut de Recherche sur les Systèmes Atomiques et Moléculaires Complexes (IRSAMC), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Fédération de recherche « Matière et interactions » (FeRMI), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), and Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)

Subjects
[PHYS.COND.GAS]Physics [physics]/Condensed Matter [cond-mat]/Quantum Gases [cond-mat.quant-gas], dispersion relation, FOS: Physical sciences, parametric, 01 natural sciences, 010305 fluids & plasmas, weak interaction, dimension, [PHYS.QPHY]Physics [physics]/Quantum Physics [quant-ph], gas, 0103 physical sciences, excited state, thermodynamical, [PHYS.COND]Physics [physics]/Condensed Matter [cond-mat], 010306 general physics, Condensed Matter - Statistical Mechanics, Quantum Physics, polaron, Statistical Mechanics (cond-mat.stat-mech), strong interaction, quasiparticle, singularity, Quantum Gases (cond-mat.quant-gas), spectral, dispersion, boson, Condensed Matter - Quantum Gases, Quantum Physics (quant-ph), soliton
Abstract

We study a one-dimensional Bose gas with two internal states described by the Yang-Gaudin model and calculate analytically the dispersion relation of a polaron quasiparticle, which is the lowest excitation branch. We study the dispersion in the thermodynamic limit in the regimes of weak and strong interaction without limitations on the momentum. At weak interaction the polaron dispersion is in the vicinity of the dark soliton one; we calculate the leading deviation in the parametric form. At strong interaction we find an ansatz for the explicit form of the polaron dispersion. It has the form of a power series of the sine function of the momentum with interaction-dependent coefficients. By increasing the power of the series, the corresponding coefficients show faster decay and thus one practically needs only a few of them; we give the results for the first three. The coefficients of the series are connected to the Maclaurin series of the polaron dispersion and thus it is sufficient to calculate latter quantity to automatically find the power series result for the dispersion at all momenta. The derived results for the dispersion can be used to obtain explicit expressions for the exponents of the power-law singularities in the response functions at the spectral edge., Comment: 8 pages, 2 figures

Published
2021
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10. Relaxation of the degenerate one-dimensional Fermi gas

Author

Konstantin I. Matveev, Zoran Ristivojevic, Materials Science Division, Argonne National Laboratory [Lemont] (ANL), Fermions Fortement Corrélés (LPT) (FFC), Laboratoire de Physique Théorique (LPT), Institut de Recherche sur les Systèmes Atomiques et Moléculaires Complexes (IRSAMC), Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche sur les Systèmes Atomiques et Moléculaires Complexes (IRSAMC), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Institut de Recherche sur les Systèmes Atomiques et Moléculaires Complexes (IRSAMC), and Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées

Subjects
Physics, Thermal equilibrium, Condensed Matter::Quantum Gases, Condensed matter physics, Condensed Matter - Mesoscale and Nanoscale Physics, Degenerate energy levels, FOS: Physical sciences, Fermi energy, 02 engineering and technology, Fermion, 021001 nanoscience & nanotechnology, 01 natural sciences, Quantum Gases (cond-mat.quant-gas), Mesoscale and Nanoscale Physics (cond-mat.mes-hall), 0103 physical sciences, Relaxation (physics), [PHYS.COND]Physics [physics]/Condensed Matter [cond-mat], Perturbation theory, 010306 general physics, 0210 nano-technology, Fermi gas, Condensed Matter - Quantum Gases, ComputingMilieux_MISCELLANEOUS, Spin-½
Abstract

We study how a system of one-dimensional spin-1/2 fermions at temperatures well below the Fermi energy approaches thermal equilibrium. The interactions between fermions are assumed to be weak and are accounted for within the perturbation theory. In the absence of an external magnetic field, spin degeneracy strongly affects relaxation of the Fermi gas. For sufficiently short-range interactions, the rate of relaxation scales linearly with temperature. Focusing on the case of the system near equilibrium, we linearize the collision integral and find exact solution of the resulting relaxation problem. We discuss the application of our results to the evaluation of the transport coefficients of the one-dimensional Fermi gas., 12 pages

Published
2020

11. Exact Results for the Boundary Energy of One-Dimensional Bosons

Author

Zoran Ristivojevic, Grigori E. Astrakharchik, Benjamin Reichert, Aleksandra Petković, Laboratoire de Physique Théorique (LPT), Institut de Recherche sur les Systèmes Atomiques et Moléculaires Complexes (IRSAMC), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Universitat Politècnica de Catalunya [Barcelona] (UPC), Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3), Universitat Politècnica de Catalunya. Departament de Física, and Universitat Politècnica de Catalunya. SIMCON - First-principles approaches to condensed matter physics: quantum effects and complexity

Subjects
[PHYS.COND.GAS]Physics [physics]/Condensed Matter [cond-mat]/Quantum Gases [cond-mat.quant-gas], Quantum Monte Carlo, Montecarlo, Mètode de, FOS: Physical sciences, General Physics and Astronomy, 01 natural sciences, Bethe ansatz, Boundary energy, Diffusion quantum Monte Carlo, 0103 physical sciences, [PHYS.COND]Physics [physics]/Condensed Matter [cond-mat], 010306 general physics, Condensed Matter - Statistical Mechanics, Mathematical Physics, Mathematical physics, Boson, Physics, [PHYS]Physics [physics], Quantum Physics, Statistical Mechanics (cond-mat.stat-mech), Física [Àrees temàtiques de la UPC], Bose gases, Mathematical Physics (math-ph), Integral equation, Universality (dynamical systems), Monte Carlo method, Exact solutions in general relativity, Quantum Gases (cond-mat.quant-gas), Thermodynamic limit, Quantum Physics (quant-ph), Condensed Matter - Quantum Gases, Exact solutions for many-body systems
Abstract

We study bosons in a one-dimensional hard-wall box potential. In the case of contact interaction, the system is exactly solvable by the Bethe ansatz, as first shown by Gaudin in 1971. Although contained in the exact solution, the boundary energy in the thermodynamic limit for this problem is only approximately calculated by Gaudin, who found the leading order result at weak repulsion. Here we derive an exact integral equation that enables one to calculate the boundary energy in the thermodynamic limit at an arbitrary interaction. We then solve such an equation and find the asymptotic results for the boundary energy at weak and strong interactions. The analytical results obtained from the Bethe ansatz are in agreement with the ones found by other complementary methods, including quantum Monte Carlo simulations. We study the universality of the boundary energy in the regime of a small gas parameter by making a comparison with the exact solution for the hard rod gas., six pages main text and three pages supplemental material; to appear in Physical Review Letters

Published
2019

12. Conjectures about the ground-state energy of the Lieb-Liniger model at weak repulsion

Author

Zoran Ristivojevic, Fermions Fortement Corrélés (LPT) (FFC), Laboratoire de Physique Théorique (LPT), Institut de Recherche sur les Systèmes Atomiques et Moléculaires Complexes (IRSAMC), Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche sur les Systèmes Atomiques et Moléculaires Complexes (IRSAMC), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse III - Paul Sabatier (UT3), and Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse)

Subjects
Chebyshev polynomials, Integrable system, [PHYS.COND.GAS]Physics [physics]/Condensed Matter [cond-mat]/Quantum Gases [cond-mat.quant-gas], FOS: Physical sciences, 02 engineering and technology, Weak interaction, 01 natural sciences, 0103 physical sciences, Lieb–Liniger model, Statistical physics, 010306 general physics, ComputingMilieux_MISCELLANEOUS, Condensed Matter - Statistical Mechanics, Mathematical Physics, Boson, Physics, Statistical Mechanics (cond-mat.stat-mech), Nonlinear Sciences - Exactly Solvable and Integrable Systems, Integer relation algorithm, Mathematical Physics (math-ph), 021001 nanoscience & nanotechnology, Integral equation, Quantum Gases (cond-mat.quant-gas), Exactly Solvable and Integrable Systems (nlin.SI), 0210 nano-technology, Ground state, Condensed Matter - Quantum Gases
Abstract

We develop an alternative description to solve the problem of the ground-state energy of the Lieb-Liniger model that describes one-dimensional bosons with contact repulsion. For this integrable model we express the Lieb integral equation in the representation of Chebyshev polynomials. The latter form is convenient to efficiently obtain very precise numerical results in the singular limit of weak interaction. Such highly precise data enable us to use the integer relation algorithm to discover the analytical form of the coefficients in the expansion of the ground-state energy for small values of the interaction parameter. We obtained the first nine terms of the expansion using quite moderate numerical efforts. The detailed knowledge of behavior of the ground-state energy on the interaction immediately leads to exact perturbative results for the excitation spectrum., four pages

Published
2019

13. Field-theoretical approach to the Casimir-like interaction in a one-dimensional Bose gas

Author

Zoran Ristivojevic, Aleksandra Petković, Benjamin Reichert, Fermions Fortement Corrélés (LPT) (FFC), Laboratoire de Physique Théorique (LPT), Institut de Recherche sur les Systèmes Atomiques et Moléculaires Complexes (IRSAMC), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche sur les Systèmes Atomiques et Moléculaires Complexes (IRSAMC), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Université Toulouse III - Paul Sabatier (UT3), and Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3)

Subjects
Physics, Quantum Physics, Strongly Correlated Electrons (cond-mat.str-el), [PHYS.COND.GAS]Physics [physics]/Condensed Matter [cond-mat]/Quantum Gases [cond-mat.quant-gas], Field (physics), Bose gas, FOS: Physical sciences, Inverse, 02 engineering and technology, 021001 nanoscience & nanotechnology, 01 natural sciences, Casimir effect, Condensed Matter - Strongly Correlated Electrons, Quantum Gases (cond-mat.quant-gas), Impurity, Quantum mechanics, 0103 physical sciences, Thermal, Bound state, Condensed Matter - Quantum Gases, Quantum Physics (quant-ph), 010306 general physics, 0210 nano-technology, Quantum, ComputingMilieux_MISCELLANEOUS
Abstract

We study the fluctuation-induced interaction between two impurities in a weakly-interacting one-dimensional Bose gas using the field theoretical approach. At separations between impurities shorter and of the order of the healing length of the system, the induced interaction has a classical origin and behaves exponentially. At separations longer than the healing length, the interaction is of a quantum origin and scales as the third power of the inverse distance. Finite temperature destroys the quasi-long-range order of the Bose gas and, accordingly, the induced interaction becomes exponentially suppressed beyond the thermal length. We obtain analytical expressions for the induced interaction at zero and finite temperature that are valid at arbitrary distances. We discuss experimental realizations as well as possible formation of bound states of two impurities, known as bipolarons., Comment: 14 pages, 1 figure; accepted to Physical Review B

Published
2019

14. The Casimir-like effect in a one-dimensional Bose gas

Author

Aleksandra Petković, Benjamin Reichert, Zoran Ristivojevic, Fermions Fortement Corrélés (LPT) (FFC), Laboratoire de Physique Théorique (LPT), Institut de Recherche sur les Systèmes Atomiques et Moléculaires Complexes (IRSAMC), Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche sur les Systèmes Atomiques et Moléculaires Complexes (IRSAMC), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Institut de Recherche sur les Systèmes Atomiques et Moléculaires Complexes (IRSAMC), and Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées

Subjects
Physics, Bose gas, Analytical expressions, [PHYS.COND.GAS]Physics [physics]/Condensed Matter [cond-mat]/Quantum Gases [cond-mat.quant-gas], General Physics and Astronomy, FOS: Physical sciences, 01 natural sciences, Power law, 010305 fluids & plasmas, Theory based, Casimir effect, Impurity, Quantum Gases (cond-mat.quant-gas), Quantum mechanics, Regularization (physics), 0103 physical sciences, 010306 general physics, Condensed Matter - Quantum Gases, Quantum fluctuation, ComputingMilieux_MISCELLANEOUS
Abstract

The electromagnetic Casimir effect manifests as the interaction between uncharged conducting objects that are placed in a vacuum. More generally, the Casimir-like effect denotes an induced interaction between external bodies in a fluctuating medium. We study the Casimir-like interaction between two impurities embedded in a weakly interacting one-dimensional Bose gas. We develop a theory based on the Gross-Pitaevskii equation that accounts for the effect of quantum fluctuations. At small separations, the induced interaction between the impurities decays exponentially with the distance. This is a classical result that can be understood using the mean-field Gross-Pitaevskii equation. We find that at larger distances, the induced interaction crosses over into a power law dependence due to the quantum fluctuations. We obtain an analytic expression for the interaction that interpolates between the two limiting behaviors. The obtained result does not require any regularization., Comment: 1 figure

Published
2019

15. Thermal conductivity of the degenerate one-dimensional Fermi gas

Author

Zoran Ristivojevic, Konstantin I. Matveev, Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439, USA, Argonne National Laboratory [Lemont] (ANL), Fermions Fortement Corrélés (LPT) (FFC), Laboratoire de Physique Théorique (LPT), Institut de Recherche sur les Systèmes Atomiques et Moléculaires Complexes (IRSAMC), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche sur les Systèmes Atomiques et Moléculaires Complexes (IRSAMC), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Université Toulouse III - Paul Sabatier (UT3), and Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3)

Subjects
Materials science, Condensed Matter - Mesoscale and Nanoscale Physics, Condensed matter physics, FOS: Physical sciences, Fermi energy, 02 engineering and technology, Fermion, Dissipation, 021001 nanoscience & nanotechnology, 01 natural sciences, 7. Clean energy, Temperature gradient, Thermal conductivity, Quantum Gases (cond-mat.quant-gas), Mesoscale and Nanoscale Physics (cond-mat.mes-hall), 0103 physical sciences, Relaxation (physics), Microscopic theory, [PHYS.COND]Physics [physics]/Condensed Matter [cond-mat], Condensed Matter - Quantum Gases, 010306 general physics, 0210 nano-technology, Fermi gas, ComputingMilieux_MISCELLANEOUS
Abstract

We study heat transport in a gas of one-dimensional fermions in the presence of a small temperature gradient. At temperatures well below the Fermi energy there are two types of relaxation processes in this system, with dramatically different relaxation rates. As a result, in addition to the usual thermal conductivity, one can introduce the thermal conductivity of the gas of elementary excitations, which quantifies the dissipation in the system in the broad range of frequencies between the two relaxation rates. We develop a microscopic theory of these transport coefficients in the limit of weak interactions between the fermions., Comment: 17 pages

Published
2019

16. Fluctuation-induced potential for an impurity in a semi-infinite one-dimensional Bose gas

Author

Zoran Ristivojevic, Benjamin Reichert, Aleksandra Petković, Fermions Fortement Corrélés (LPT) (FFC), Laboratoire de Physique Théorique (LPT), Institut de Recherche sur les Systèmes Atomiques et Moléculaires Complexes (IRSAMC), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Institut de Recherche sur les Systèmes Atomiques et Moléculaires Complexes (IRSAMC), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées, Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3), and Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche sur les Systèmes Atomiques et Moléculaires Complexes (IRSAMC)

Subjects
Bose gas, FOS: Physical sciences, 02 engineering and technology, 01 natural sciences, Interaction potential, Impurity, Condensed Matter::Superconductivity, 0103 physical sciences, nanoscale physics, 010306 general physics, Surface physics, Condensed Matter - Statistical Mechanics, Boson, Physics, Strongly coupled, Statistical Mechanics (cond-mat.stat-mech), Condensed matter physics, Semi-infinite, Scattering, low-dimensional systems, 021001 nanoscience & nanotechnology, Condensed Matter::Mesoscopic Systems and Quantum Hall Effect, [PHYS.PHYS.PHYS-GEN-PH]Physics [physics]/Physics [physics]/General Physics [physics.gen-ph], 3. Good health, Quantum Gases (cond-mat.quant-gas), Condensed Matter::Strongly Correlated Electrons, 0210 nano-technology, Condensed Matter - Quantum Gases
Abstract

We consider an impurity in a semi-infinite one-dimensional system of weakly-interacting bosons. We calculate the interaction potential for the impurity due to the end of the system, i.e., the wall. For local repulsive (attractive) interaction between the impurity and the Bose gas, the interaction potential is attractive (repulsive). At short distances from the wall it decays exponentially crossing over into a universal $1/r^2$ behavior at separations $r$ above the healing length. Our results can also be interpreted as a Casimir-like interaction between two impurities, where one of them is infinitely strongly coupled to the Bose gas. We discuss various scenarios for the induced interaction between the impurities using the scattering approach. We finally address the phenomenon of localization of the impurity near the wall. In the paper we mainly study the case of a static impurity, however the universal $1/r^2$ interaction also holds for a slowly moving impurity., 7 pages main text and 2 pages supplemental material; to appear in Physical Review B

Published
2019

17. Quasiparticle decay in a one-dimensional Bose-Fermi mixture

Author

Aleksandra Petković, Benjamin Reichert, Zoran Ristivojevic, Fermions Fortement Corrélés (LPT) (FFC), Laboratoire de Physique Théorique (LPT), Institut de Recherche sur les Systèmes Atomiques et Moléculaires Complexes (IRSAMC), Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche sur les Systèmes Atomiques et Moléculaires Complexes (IRSAMC), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Institut de Recherche sur les Systèmes Atomiques et Moléculaires Complexes (IRSAMC), and Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées

Subjects
Condensed Matter::Quantum Gases, Physics, [PHYS.COND.GAS]Physics [physics]/Condensed Matter [cond-mat]/Quantum Gases [cond-mat.quant-gas], Condensed matter physics, Branching fraction, Phonon, FOS: Physical sciences, Fermion, Condensed Matter::Mesoscopic Systems and Quantum Hall Effect, 01 natural sciences, 010305 fluids & plasmas, Momentum, Quantum Gases (cond-mat.quant-gas), Excited state, 0103 physical sciences, Quasiparticle, High Energy Physics::Experiment, Condensed Matter::Strongly Correlated Electrons, Microscopic theory, Condensed Matter - Quantum Gases, 010306 general physics, Scaling, ComputingMilieux_MISCELLANEOUS
Abstract

In a one-dimensional weakly interacting Bose-Fermi mixture one branch of elementary excitations is well described by the Bogoliubov spectrum. Here we use the microscopic theory to study the decay of such quasiparticle excitations. The main scattering process which leads to their decay is the backscattering of a Bogoliubov quasiparticle off the Fermi sea, where a particle-hole pair is excited. For a low-momentum quasiparticle (phonon) of momentum $q$, we find that the decay rate scales as $q^3$ provided $q$ is smaller than the Fermi momentum $k_F$, while in the opposite case the decay behaves as $q^2$. If the ratio of the masses of fermions and bosons equals to the ratio of the boson-fermion and the boson-boson interaction strengths, the decay rate changes dramatically. It scales as $q^7$ for $qk_F$. For a high momentum Bogoliubov quasiparticle, we find a constant decay rate for $qk_F$. We also find an analytic expression for the decay rate in the crossover region between low and high momenta. The decay rate is a continuous, but nonanalytic function of the momentum at $q=k_F$. In the special case when the parameters of our system correspond to the integrable model, we observe that the decay rate vanishes., Comment: 14 pages

Published
2017

18. Dynamics of a Mobile Impurity in a One-Dimensional Bose Liquid

Author

Aleksandra Petković, Zoran Ristivojevic, Fermions Fortement Corrélés (LPT) (FFC), Laboratoire de Physique Théorique (LPT), Institut de Recherche sur les Systèmes Atomiques et Moléculaires Complexes (IRSAMC), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Institut de Recherche sur les Systèmes Atomiques et Moléculaires Complexes (IRSAMC), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées, Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche sur les Systèmes Atomiques et Moléculaires Complexes (IRSAMC), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Université Toulouse III - Paul Sabatier (UT3), and Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3)

Subjects
Physics, Strongly Correlated Electrons (cond-mat.str-el), Condensed matter physics, [PHYS.COND.GAS]Physics [physics]/Condensed Matter [cond-mat]/Quantum Gases [cond-mat.quant-gas], Scattering, FOS: Physical sciences, General Physics and Astronomy, Kinetic energy, 01 natural sciences, Linear function, 010305 fluids & plasmas, Condensed Matter - Strongly Correlated Electrons, Quantum Gases (cond-mat.quant-gas), Impurity, Excited state, 0103 physical sciences, Quasiparticle, Microscopic theory, 010306 general physics, Condensed Matter - Quantum Gases, Quantum, ComputingMilieux_MISCELLANEOUS
Abstract

We develop a microscopic theory of a quantum impurity propagating in a one-dimensional Bose liquid. As a result of scattering off thermally excited quasiparticles, the impurity experiences the friction. We find that, at low temperatures, the resulting force scales either as the fourth or the eighth power of temperature, depending on the system parameters. For temperatures higher than the chemical potential of the Bose liquid, the friction force is a linear function of temperature. Our approach enables us to find the friction force in the crossover region between the two limiting cases. In the integrable case, corresponding to the Yang-Gaudin model, the impurity becomes transparent for quasiparticles and thus the friction force is absent. Our results could be further generalized to study other kinetic phenomena., 5 pages and 1 figure

Published
2016

19. Decay of Bogoliubov excitations in one-dimensional Bose gases

Author

Zoran Ristivojevic, Konstantin I. Matveev, Fermions Fortement Corrélés (LPT) (FFC), Laboratoire de Physique Théorique (LPT), Institut de Recherche sur les Systèmes Atomiques et Moléculaires Complexes (IRSAMC), Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche sur les Systèmes Atomiques et Moléculaires Complexes (IRSAMC), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Material Science Division [ANL] (MSD), Argonne National Laboratory [Lemont] (ANL), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Institut de Recherche sur les Systèmes Atomiques et Moléculaires Complexes (IRSAMC), and Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées

Subjects
Condensed Matter::Quantum Gases, Physics, [PHYS.COND.GAS]Physics [physics]/Condensed Matter [cond-mat]/Quantum Gases [cond-mat.quant-gas], Integrable system, Phonon, FOS: Physical sciences, Rate of decay, 01 natural sciences, 010305 fluids & plasmas, symbols.namesake, Quantum Gases (cond-mat.quant-gas), Condensed Matter::Superconductivity, Quantum electrodynamics, 0103 physical sciences, Quasiparticle, symbols, Microscopic theory, Zero temperature, Condensed Matter - Quantum Gases, 010306 general physics, Hamiltonian (quantum mechanics), ComputingMilieux_MISCELLANEOUS, Boson
Abstract

We study the decay of Bogoliubov quasiparticles in one-dimensional Bose gases. Starting from the hydrodynamic Hamiltonian, we develop a microscopic theory that enables one to systematically study both the excitations and their decay. At zero temperature, the leading mechanism of decay of a quasiparticle is disintegration into three others. We find that low-energy quasiparticles (phonons) decay with the rate that scales with the seventh power of momentum, whereas the rate of decay of the high-energy quasiparticles does not depend on momentum. In addition, our approach allows us to study analytically the quasiparticle decay in the whole crossover region between the two limiting cases. When applied to integrable models, including the Lieb-Liniger model of bosons with contact repulsion, our theory confirms the absence of the decay of quasiparticle excitations. We account for two types of integrability-breaking perturbations that enable finite decay: three-body interaction between the bosons and two-body interaction of finite range., 17 pages

Published
2016

20. Cross sections and transport properties of Cl- ions in noble gases

Author

Z. Lj. Petrović, Jasmina Jovanovic, Zoran Ristivojevic, Vladimir Stojanovic, and Zoran Raspopovic

Subjects
Elastic scattering, Materials science, Transport coefficient, Monte Carlo method, Momentum transfer, Halogen, Optical physics, Plasma, Atomic physics, Atomic and Molecular Physics, and Optics, Ion
Abstract

We have used a simple semi-analytic — momentum transfer theory (MTT) to develop negative halogen ions/noble gases momentum transfer integral cross sections based on the available data for reduced mobility at 300 K as a function of E/N. The unfolded cross sections were validated or further improved by assuring a good agreement between our Monte Carlo (MC) calculated transport data and the available experimental results. The data are produced with an aim to provide plasma modellers with cross section data and transport coefficients. We have also calculated the net rates of elastic scattering and detachment.

Published
2008

21. Decay of Bogoliubov quasiparticles in a nonideal one-dimensional Bose gas

Author

Konstantin I. Matveev, Zoran Ristivojevic, Fermions Fortement Corrélés (LPT) (FFC), Laboratoire de Physique Théorique (LPT), Institut de Recherche sur les Systèmes Atomiques et Moléculaires Complexes (IRSAMC), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche sur les Systèmes Atomiques et Moléculaires Complexes (IRSAMC), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Centre de Physique Théorique [Palaiseau] (CPHT), Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X), Material Science Division [ANL] (MSD), Argonne National Laboratory [Lemont] (ANL), Université Toulouse III - Paul Sabatier (UT3), and Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3)

Subjects
[PHYS.COND.GAS]Physics [physics]/Condensed Matter [cond-mat]/Quantum Gases [cond-mat.quant-gas], Integrable system, Bose gas, Phonon, FOS: Physical sciences, 01 natural sciences, 010305 fluids & plasmas, Momentum, Condensed Matter - Strongly Correlated Electrons, Condensed Matter::Superconductivity, Quantum mechanics, Mesoscale and Nanoscale Physics (cond-mat.mes-hall), 0103 physical sciences, 010306 general physics, Boson, Physics, Conservation law, Condensed Matter - Mesoscale and Nanoscale Physics, Strongly Correlated Electrons (cond-mat.str-el), Condensed Matter Physics, Electronic, Optical and Magnetic Materials, Quantum Gases (cond-mat.quant-gas), Quantum electrodynamics, Quasiparticle, Relaxation (physics), Condensed Matter::Strongly Correlated Electrons, Condensed Matter - Quantum Gases
Abstract

We study the relaxation of excitations in a system of one-dimensional weakly interacting bosons. Due to residual weak interactions, Bogoliubov quasiparticles in this system have finite lifetimes. As a result of the conservation laws in one dimension, at zero temperature the leading mechanism of decay of a quasiparticle is disintegration into three others. We focus on phonon quasiparticles and find that their decay rate is proportional to the seventh power of momentum. In the integrable case of contact interaction between the bosons, the decay rate vanishes., Comment: four pages, one figure

Published
2014

22. Superfluid/Bose-glass transition in one dimension

Author

Pierre Le Doussal, Zoran Ristivojevic, Thierry Giamarchi, Aleksandra Petković, Centre de Physique Théorique [Palaiseau] (CPHT), Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X), Fermions Fortement Corrélés (LPT) (FFC), Laboratoire de Physique Théorique (LPT), Institut de Recherche sur les Systèmes Atomiques et Moléculaires Complexes (IRSAMC), Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche sur les Systèmes Atomiques et Moléculaires Complexes (IRSAMC), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Physique Théorique de l'ENS (LPTENS), Université Pierre et Marie Curie - Paris 6 (UPMC)-Fédération de recherche du Département de physique de l'Ecole Normale Supérieure - ENS Paris (FRDPENS), Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS), Département de Physique de la Matière Condensée (DPMC), Université de Genève (UNIGE), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Centre National de la Recherche Scientifique (CNRS), École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS), Université de Toulouse (UT)-Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche sur les Systèmes Atomiques et Moléculaires Complexes (IRSAMC), Université de Toulouse (UT)-Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Physique Théorique de l'ENS [École Normale Supérieure] (LPTENS), Fédération de recherche du Département de physique de l'Ecole Normale Supérieure - ENS Paris (FRDPENS), École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Centre National de la Recherche Scientifique (CNRS), and Université de Genève = University of Geneva (UNIGE)

Subjects
Quantum phase transition, Logarithm, [PHYS.COND.GAS]Physics [physics]/Condensed Matter [cond-mat]/Quantum Gases [cond-mat.quant-gas], FOS: Physical sciences, ddc:500.2, 01 natural sciences, 010305 fluids & plasmas, Superfluidity, Phase (matter), 0103 physical sciences, [PHYS.COND.CM-SM]Physics [physics]/Condensed Matter [cond-mat]/Statistical Mechanics [cond-mat.stat-mech], 010306 general physics, Condensed Matter - Statistical Mechanics, Phase diagram, Boson, Physics, Statistical Mechanics (cond-mat.stat-mech), Condensed matter physics, Disordered Systems and Neural Networks (cond-mat.dis-nn), Renormalization group, Condensed Matter - Disordered Systems and Neural Networks, Condensed Matter Physics, Electronic, Optical and Magnetic Materials, Quantum Gases (cond-mat.quant-gas), Glass transition, Condensed Matter - Quantum Gases
Abstract

We consider a one-dimensional system of interacting bosons in a random potential. At zero temperature, it can be either in the superfluid or in the insulating phase. We study the transition at weak disorder and moderate interaction. Using a systematic approach, we derive the renormalization group equations at two-loop order and discuss the phase diagram. We find the universal form of the correlation functions at the transitions and compute the logarithmic corrections to the main universal power-law behavior. In order to mimic large density fluctuations on a single site, we study a simplified model of disordered two-leg bosonic ladders with correlated disorder across the rung. Contrarily to the single-chain case, the latter system exhibits a transition between a superfluid and a localized phase where the exponents of the correlation functions at the transition do not take universal values., 21 pages, 3 figures

Published
2014

23. Excitation spectrum of the Lieb-Liniger model

Author

Zoran Ristivojevic, Fermions Fortement Corrélés (LPT) (FFC), Laboratoire de Physique Théorique (LPT), Institut de Recherche sur les Systèmes Atomiques et Moléculaires Complexes (IRSAMC), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche sur les Systèmes Atomiques et Moléculaires Complexes (IRSAMC), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Centre de Physique Théorique [Palaiseau] (CPHT), Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X), Université Toulouse III - Paul Sabatier (UT3), and Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3)

Subjects
Physics, Condensed Matter::Quantum Gases, [PHYS.COND.GAS]Physics [physics]/Condensed Matter [cond-mat]/Quantum Gases [cond-mat.quant-gas], Strong interaction, General Physics and Astronomy, FOS: Physical sciences, Fermion, Weak interaction, Momentum, Quantum Gases (cond-mat.quant-gas), Quantum mechanics, Quantum electrodynamics, Quasiparticle, Lieb–Liniger model, Condensed Matter - Quantum Gases, Asymptotic expansion, Boson
Abstract

We study the integrable model of one-dimensional bosons with contact repulsion. In the limit of weak interaction, we use the microscopic hydrodynamic theory to obtain the excitation spectrum. The statistics of quasiparticles changes with the increase of momentum. At lowest momenta good quasiparticles are fermions, while at higher momenta they are Bogoliubov bosons, in accordance with recent studies. In the limit of strong interaction, we analyze the exact solution and find exact results for the spectrum in terms of the asymptotic series. Those results undoubtedly suggest that fermionic quasiparticle excitations actually exist at all momenta for moderate and strong interaction, and also at lowest momenta for arbitrary interaction. Moreover, at strong interaction we find highly accurate analytical results for several relevant quantities of the Lieb-Liniger model., Comment: seven pages and two figures

Published
2014
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24. Relaxation of weakly interacting electrons in one dimension

Author

Zoran Ristivojevic and Konstantin I. Matveev

Subjects
Physics, Quantum Physics, Strongly Correlated Electrons (cond-mat.str-el), Condensed Matter - Mesoscale and Nanoscale Physics, Scattering, Nonlinear dispersion, FOS: Physical sciences, Electron, Condensed Matter Physics, Electronic, Optical and Magnetic Materials, Condensed Matter - Strongly Correlated Electrons, Dimension (vector space), Mesoscale and Nanoscale Physics (cond-mat.mes-hall), Quasiparticle, Coulomb, Relaxation (physics), Atomic physics, Quantum Physics (quant-ph), Excitation
Abstract

We consider the problem of relaxation in a one-dimensional system of interacting electrons. In the limit of weak interactions, we calculate the decay rate of a single-electron excitation, accounting for the nonlinear dispersion. The leading processes that determine the relaxation involve scattering of three particles. We elucidate how particular forms of Coulomb interaction, unscreened and screened, lead to different results for the decay rates and identify the dominant scattering processes responsible for relaxation of excitations of different energies. Interestingly, temperatures much smaller than the excitation energy strongly affect the rate. At higher temperatures the quasiparticle relaxes by exciting copropagating electron-hole pairs, whereas at lowest temperatures the relaxation proceeds via excitations of both copropagating and counterpropagating pairs., 5 pages, 2 figures

Published
2013

25. Exact form of the exponential correlation function in the glassy super-rough phase

Author

Kay Jörg Wiese, Zoran Ristivojevic, Pierre Le Doussal, Laboratoire de Physique Théorique de l'ENS (LPTENS), Fédération de recherche du Département de physique de l'Ecole Normale Supérieure - ENS Paris (FRDPENS), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Euler–Mascheroni constant, FOS: Physical sciences, Correlation function (quantum field theory), 01 natural sciences, Condensed Matter::Disordered Systems and Neural Networks, 010305 fluids & plasmas, Combinatorics, symbols.namesake, Quantum mechanics, 0103 physical sciences, [PHYS.COND.CM-DS-NN]Physics [physics]/Condensed Matter [cond-mat]/Disordered Systems and Neural Networks [cond-mat.dis-nn], [PHYS.COND]Physics [physics]/Condensed Matter [cond-mat], 010306 general physics, Condensed Matter - Statistical Mechanics, Physics, [PHYS]Physics [physics], Statistical Mechanics (cond-mat.stat-mech), Order (ring theory), Condensed Matter Physics, Electronic, Optical and Magnetic Materials, Exponential function, Closed and exact differential forms, Riemann hypothesis, Digamma function, symbols, Exponent
Abstract

We consider the random-phase sine-Gordon model in two dimensions. It describes two-dimensional elastic systems with random periodic disorder, such as pinned flux-line arrays, random field XY models, and surfaces of disordered crystals. The model exhibits a super-rough glass phase at low temperature $T, Comment: 19 pages, 9 figures

Published
2013
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26. Super-rough phase of the random-phase sine-Gordon model: Two-loop results

Author

Pierre Le Doussal, Kay Jörg Wiese, Zoran Ristivojevic, Laboratoire de Physique Théorique de l'ENS (LPTENS), Fédération de recherche du Département de physique de l'Ecole Normale Supérieure - ENS Paris (FRDPENS), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)

Subjects
[PHYS]Physics [physics], Physics, Statistical Mechanics (cond-mat.stat-mech), Condensed matter physics, Anharmonicity, FOS: Physical sciences, Disordered Systems and Neural Networks (cond-mat.dis-nn), Condensed Matter - Disordered Systems and Neural Networks, Renormalization group, Condensed Matter Physics, 01 natural sciences, 010305 fluids & plasmas, Electronic, Optical and Magnetic Materials, Loop (topology), Amplitude, Correlation function, Phase (matter), 0103 physical sciences, Exponent, [PHYS.COND.CM-DS-NN]Physics [physics]/Condensed Matter [cond-mat]/Disordered Systems and Neural Networks [cond-mat.dis-nn], [PHYS.COND]Physics [physics]/Condensed Matter [cond-mat], 010306 general physics, Random phase approximation, Condensed Matter - Statistical Mechanics
Abstract

We consider the two-dimensional random-phase sine-Gordon and study the vicinity of its glass transition temperature $T_c$, in an expansion in small $\tau=(T_c-T)/T_c$, where $T$ denotes the temperature. We derive renormalization group equations in cubic order in the anharmonicity, and show that they contain two universal invariants. Using them we obtain that the correlation function in the super-rough phase for temperature $T} = \mathcal{A}\ln^2(|x|/a) + \mathcal{O}[\ln(|x|/a)]$, where the amplitude $\mathcal{A}$ is a universal function of temperature $\mathcal{A}=2\tau^2-2\tau^3+\mathcal{O}(\tau^4)$. This result differs at two-loop order, i.e., $\mathcal{O}(\tau^3)$, from the prediction based on results from the "nearly conformal" field theory of a related fermion model. We also obtain the correction-to-scaling exponent., Comment: 34 pages

Published
2012

27. Multigrid algorithms for tensor network states

Author

Bela Bauer, Zoran Ristivojevic, Michele Dolfi, and Matthias Troyer

Subjects
Physics, Optical lattice, Strongly Correlated Electrons (cond-mat.str-el), Density matrix renormalization group, High Energy Physics::Lattice, FOS: Physical sciences, General Physics and Astronomy, Renormalization group, Condensed Matter - Strongly Correlated Electrons, Amplitude, Quantum Gases (cond-mat.quant-gas), Lattice (order), Quantum mechanics, Strongly correlated material, Statistical physics, Condensed Matter - Quantum Gases, Lattice model (physics), Boson
Abstract

The widely used density matrix renormalization group (DRMG) method often fails to converge in systems with multiple length scales, such as lattice discretizations of continuum models and dilute or weakly doped lattice models. The local optimization employed by DMRG to optimize the wave function is ineffective in updating large-scale features. Here we present a multigrid algorithm that solves these convergence problems by optimizing the wave function at different spatial resolutions. We demonstrate its effectiveness by simulating bosons in continuous space, and study non-adiabaticity when ramping up the amplitude of an optical lattice. The algorithm can be generalized to tensor network methods, and be combined with the contractor renormalization group (CORE) method to study dilute and weakly doped lattice models., 5 pages, 7 figures. Accepted for publication in PRL

Published
2012

28. Exact asymptotic behavior of correlation functions for disordered spin-1/2 XXZ chains

Author

Aleksandra Petković, Zoran Ristivojevic, Thierry Giamarchi, Laboratoire de Physique Théorique de l'ENS (LPTENS), Université Pierre et Marie Curie - Paris 6 (UPMC)-Fédération de recherche du Département de physique de l'Ecole Normale Supérieure - ENS Paris (FRDPENS), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Centre National de la Recherche Scientifique (CNRS), Département de Physique de la Matière Condensée (DPMC), Université de Genève (UNIGE), Laboratoire de Physique Théorique de l'ENS [École Normale Supérieure] (LPTENS), Fédération de recherche du Département de physique de l'Ecole Normale Supérieure - ENS Paris (FRDPENS), École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Centre National de la Recherche Scientifique (CNRS), and Université de Genève = University of Geneva (UNIGE)

Subjects
Nuclear and High Energy Physics, Logarithm, Phase (waves), FOS: Physical sciences, ddc:500.2, 01 natural sciences, Power law, Condensed Matter::Disordered Systems and Neural Networks, 010305 fluids & plasmas, [PHYS.QPHY]Physics [physics]/Quantum Physics [quant-ph], 0103 physical sciences, Limit (mathematics), [PHYS.COND.CM-SM]Physics [physics]/Condensed Matter [cond-mat]/Statistical Mechanics [cond-mat.stat-mech], 010306 general physics, Anisotropy, Condensed Matter - Statistical Mechanics, Spin-½, Mathematical physics, Physics, Quantum Physics, Statistical Mechanics (cond-mat.stat-mech), Condensed matter physics, Operator (physics), Disordered Systems and Neural Networks (cond-mat.dis-nn), Condensed Matter - Disordered Systems and Neural Networks, Symmetry (physics), Quantum Physics (quant-ph)
Abstract

We consider an XXZ spin-1/2 chain in the presence of several types of disorder that do not break the XY symmetry of the system. We calculate the complete asymptotic form of the spin-correlation functions at zero temperature at the transition between liquid and disordered phase that occurs for a special value of anisotropy in the limit of small disorder. Apart from a universal power law decay of correlations, we find additional logarithmic corrections due to marginally irrelevant operator of disorder., 11 pages

Published
2012

29. Super-Rough Glassy Phase of the Random Field XY Model in Two Dimensions

Author

Kay Joerg Wiese, Zoran Ristivojevic, Grégory Schehr, Pierre Le Doussal, Anthony Perret, Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), Centre National de la Recherche Scientifique (CNRS)-Université Paris-Sud - Paris 11 (UP11), Laboratoire de Physique Théorique de l'ENS (LPTENS), Université Pierre et Marie Curie - Paris 6 (UPMC)-Fédération de recherche du Département de physique de l'Ecole Normale Supérieure - ENS Paris (FRDPENS), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Centre National de la Recherche Scientifique (CNRS), Université Paris-Sud - Paris 11 (UP11)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Physique Théorique de l'ENS [École Normale Supérieure] (LPTENS), Fédération de recherche du Département de physique de l'Ecole Normale Supérieure - ENS Paris (FRDPENS), École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS-PSL), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Length scale, Physics, Random field, Statistical Mechanics (cond-mat.stat-mech), FOS: Physical sciences, General Physics and Astronomy, Disordered Systems and Neural Networks (cond-mat.dis-nn), Condensed Matter - Disordered Systems and Neural Networks, Renormalization group, Classical XY model, 01 natural sciences, Polynomial algorithm, 010305 fluids & plasmas, Vortex, Universality (dynamical systems), Amplitude, Quantum mechanics, 0103 physical sciences, [PHYS.COND.CM-SM]Physics [physics]/Condensed Matter [cond-mat]/Statistical Mechanics [cond-mat.stat-mech], 010306 general physics, Condensed Matter - Statistical Mechanics
Abstract

We study both analytically, using the renormalization group (RG) to two loop order, and numerically, using an exact polynomial algorithm, the disorder-induced glass phase of the two-dimensional XY model with quenched random symmetry-breaking fields and without vortices. In the super-rough glassy phase, i.e. below the critical temperature $T_c$, the disorder and thermally averaged correlation function $B(r)$ of the phase field $\theta(x)$, $B(r) = \bar{}$ behaves, for $r \gg a$, as $B(r) \simeq A(\tau) \ln^2 (r/a)$ where $r = |r|$ and $a$ is a microscopic length scale. We derive the RG equations up to cubic order in $\tau = (T_c-T)/T_c$ and predict the universal amplitude ${A}(\tau) = 2\tau^2-2\tau^3 + {\cal O}(\tau^4)$. The universality of $A(\tau)$ results from nontrivial cancellations between nonuniversal constants of RG equations. Using an exact polynomial algorithm on an equivalent dimer version of the model we compute ${A}(\tau)$ numerically and obtain a remarkable agreement with our analytical prediction, up to $\tau \approx 0.5$., Comment: 5 pages, 3 figures

Published
2012

30. Phase Transition of Interacting Disordered Bosons in One Dimension

Author

Aleksandra Petković, Pierre Le Doussal, Zoran Ristivojevic, Thierry Giamarchi, Laboratoire de Physique Théorique de l'ENS (LPTENS), Université Pierre et Marie Curie - Paris 6 (UPMC)-Fédération de recherche du Département de physique de l'Ecole Normale Supérieure - ENS Paris (FRDPENS), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Centre National de la Recherche Scientifique (CNRS), Département de Physique de la Matière Condensée (DPMC), Université de Genève (UNIGE), Laboratoire de Physique Théorique de l'ENS [École Normale Supérieure] (LPTENS), Fédération de recherche du Département de physique de l'Ecole Normale Supérieure - ENS Paris (FRDPENS), École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Centre National de la Recherche Scientifique (CNRS), and Université de Genève = University of Geneva (UNIGE)

Subjects
Bosonization, Quantum phase transition, Phase transition, [PHYS.COND.GAS]Physics [physics]/Condensed Matter [cond-mat]/Quantum Gases [cond-mat.quant-gas], General Physics and Astronomy, FOS: Physical sciences, ddc:500.2, Fixed point, 01 natural sciences, 010305 fluids & plasmas, 0103 physical sciences, Statistical physics, 010306 general physics, Scaling, Condensed Matter - Statistical Mechanics, Mathematical physics, Phase diagram, Boson, Physics, Condensed Matter::Quantum Gases, Statistical Mechanics (cond-mat.stat-mech), Disordered Systems and Neural Networks (cond-mat.dis-nn), Condensed Matter - Disordered Systems and Neural Networks, Renormalization group, Quantum Gases (cond-mat.quant-gas), Condensed Matter - Quantum Gases
Abstract

Interacting bosons generically form a superfluid state. In the presence of disorder it can get converted into a compressible Bose glass state. Here we study such transition in one dimension at moderate interaction using bosonization and renormalization group techniques. We derive the two-loop scaling equations and discuss the phase diagram. We find that the correlation functions at the transition are characterized by universal exponents in a finite region around the fixed point., Comment: five pages and two pages and one figure

Published
2012

31. Interaction effects on thermal transport in quantum wires

Author

Zoran Ristivojevic, Tobias Micklitz, Alex Levchenko, and Konstantin I. Matveev

Subjects
Physics, Condensed Matter - Mesoscale and Nanoscale Physics, Condensed matter physics, Scattering, FOS: Physical sciences, Electron, Condensed Matter Physics, Electronic, Optical and Magnetic Materials, Distribution function, Thermalisation, Thermal conductivity, Mesoscale and Nanoscale Physics (cond-mat.mes-hall), Relaxation (physics), Atomic physics, Fermi gas, Quantum
Abstract

We develop a theory of thermal transport of weakly interacting electrons in quantum wires. Unlike higher-dimensional systems, a one-dimensional electron gas requires three-particle collisions for energy relaxation. The fastest relaxation is provided by the intrabranch scattering of comoving electrons which establishes a partially equilibrated form of the distribution function. The thermal conductance is governed by the slower interbranch processes which enable energy exchange between counterpropagating particles. We derive an analytic expression for the thermal conductance of interacting electrons valid for arbitrary relation between the wire length and electron thermalization length. We find that in sufficiently long wires the interaction-induced correction to the thermal conductance saturates to an interaction-independent value., Comment: 14 pages, 4 figures

Published
2011
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32. Proposal to detect vortices above the superconducting transition temperature

Author

Zoran Ristivojevic and M. R. Norman

Subjects
Physics, Superconductivity, Condensed matter physics, Condensed Matter - Superconductivity, Transition temperature, FOS: Physical sciences, Observable, Atmospheric temperature range, Condensed Matter Physics, Electronic, Optical and Magnetic Materials, Vortex, Magnetic field, Superconductivity (cond-mat.supr-con), Condensed Matter::Superconductivity, Cuprate, Pseudogap
Abstract

We propose a simple experiment to determine whether vortices persist above the superconducting transition temperature Tc in the pseudogap phase of high temperature cuprate superconductors. This involves using a magnetic dot to stabilize a vortex in a thin cuprate film beneath the dot. We calculate the magnetic field profile as a function of distance from the dot if a vortex is present, and discuss possible measurements that could be done to detect this. Finally, we comment on the temperature range where a stable vortex should be observable., 3 pages, 2 figures

Published
2010

33. Interaction-induced corrections to conductance and thermopower in quantum wires

Author

Zoran Ristivojevic, Tobias Micklitz, and Alex Levchenko

Subjects
Physics, Conservation law, Condensed Matter - Mesoscale and Nanoscale Physics, Condensed matter physics, Scattering, Conductance, FOS: Physical sciences, Electron, Condensed Matter Physics, Electronic, Optical and Magnetic Materials, Scattering amplitude, Distribution function, Quantum electrodynamics, Mesoscale and Nanoscale Physics (cond-mat.mes-hall), Perturbation theory (quantum mechanics), Quantum
Abstract

We study transport properties of weakly interacting spinless electrons in one-dimensional single channel quantum wires. The effects of interaction manifest as three-particle collisions due to the severe constraints imposed by the conservation laws on the two-body processes. We focus on short wires where the effects of equilibration on the distribution function can be neglected and collision integral can be treated in perturbation theory. We find that interaction-induced corrections to conductance and thermopower rely on the scattering processes that change number of right- and left-moving electrons. The latter requires transition at the bottom of the band which is exponentially suppressed at low temperatures. Our theory is based on the scattering approach that is beyond the Luttinger-liquid limit. We emphasize the crucial role of the exchange terms in the three-particle scattering amplitude that was not discussed in the previous studies., Comment: 4 pages, 2 figures

Published
2010
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34. Superconducting film with randomly magnetized dots: A realization of the two-dimensionalXYmodel with random phase shifts

Author

Zoran Ristivojevic

Subjects
Physics, Surface (mathematics), Superconductivity, Condensed matter physics, Phase (waves), Condensed Matter::Mesoscopic Systems and Quantum Hall Effect, Condensed Matter Physics, Classical XY model, Electronic, Optical and Magnetic Materials, Vortex, Magnetic dots, Magnetization, Condensed Matter::Superconductivity, Realization (systems)
Abstract

We consider a thin superconducting film with randomly magnetized dots on top of it. The dots produce a disordered pinning potential for vortices in the film. We show that for dots with permanent and random magnetization normal or parallel to the film surface, our system is an experimental realization of the two-dimensional $XY$ model with random phase shifts. The low-temperature superconducting phase, that exists without magnetic dots, survives in the presence of magnetic dots for sufficiently small disorder.

Published
2009

35. Transport in a Luttinger liquid with dissipation: Two impurities

Author

Thomas Nattermann, Zoran Ristivojevic, and Leiming Chen

Subjects
Physics, Strongly Correlated Electrons (cond-mat.str-el), Condensed matter physics, FOS: Physical sciences, Conductance, Disordered Systems and Neural Networks (cond-mat.dis-nn), Electron, Condensed Matter - Disordered Systems and Neural Networks, Dissipation, Condensed Matter::Mesoscopic Systems and Quantum Hall Effect, Condensed Matter Physics, Thermal conduction, Resonance (particle physics), Electronic, Optical and Magnetic Materials, Condensed Matter - Strongly Correlated Electrons, Luttinger liquid, Impurity, Condensed Matter::Strongly Correlated Electrons, Voltage
Abstract

We consider theoretically the transport in a one-channel spinless Luttinger liquid with two strong impurities in the presence of dissipation. As a difference with respect to the dissipation free case, where the two impurities fully transmit electrons at resonance points, the dissipation prevents complete transmission in the present situation. A rich crossover diagram for the conductance as a function of applied voltage, temperature, dissipation strength, Luttinger liquid parameter K and the deviation from the resonance condition is obtained. For weak dissipation and 1/2, Comment: 11 pages, 3 figures

Published
2009

36. Spin-filtering by field dependent resonant tunneling

Author

Zoran Ristivojevic, Thomas Nattermann, and George I. Japaridze

Subjects
Physics, Condensed matter physics, Spin polarization, Strongly Correlated Electrons (cond-mat.str-el), Condensed Matter - Mesoscale and Nanoscale Physics, Quantum wire, General Physics and Astronomy, FOS: Physical sciences, Electron, Parameter space, Polarization (waves), Magnetic field, Condensed Matter - Strongly Correlated Electrons, Mesoscale and Nanoscale Physics (cond-mat.mes-hall), Quantum tunnelling, Voltage
Abstract

We consider theoretically transport in a spinfull one-channel interacting quantum wire placed in an external magnetic field. For the case of two point-like impurities embedded in the wire, under a small voltage bias the spin-polarized current occurs at special points in the parameter space, tunable by a single parameter. At sufficiently low temperatures complete spin-polarization may be achieved, provided repulsive interaction between electrons is not too strong., 4 pages, 2 figures

Published
2009

37. A Monte Carlo simulation of ion transport at finite temperatures

Author

Zoran Lj. Petrovic and Zoran Ristivojevic

Subjects
010302 applied physics, Physics, Range (particle radiation), Monte Carlo method, FOS: Physical sciences, Plasma, Computational Physics (physics.comp-ph), Condensed Matter Physics, 01 natural sciences, 7. Clean energy, Boltzmann equation, Physics - Plasma Physics, 010305 fluids & plasmas, Ion, Computational physics, Plasma Physics (physics.plasm-ph), Distribution function, Collision frequency, 0103 physical sciences, Piecewise, Physics - Computational Physics
Abstract

We have developed a Monte Carlo simulation for ion transport in hot background gases, which is an alternative way of solving the corresponding Boltzmann equation that determines the distribution function of ions. We consider the limit of low ion densities when the distribution function of the background gas remains unchanged due to collision with ions. A special attention has been paid to properly treat the thermal motion of the host gas particles and their influence on ions, which is very important at low electric fields, when the mean ion energy is comparable to the thermal energy of the host gas. We found the conditional probability distribution of gas velocities that correspond to an ion of specific velocity which collides with a gas particle. Also, we have derived exact analytical formulas for piecewise calculation of the collision frequency integrals. We address the cases when the background gas is monocomponent and when it is a mixture of different gases. The developed techniques described here are required for Monte Carlo simulations of ion transport and for hybrid models of non-equilibrium plasmas. The range of energies where it is necessary to apply the technique has been defined. The results we obtained are in excellent agreement with the existing ones obtained by complementary methods. Having verified our algorithm, we were able to produce calculations for Ar$^+$ ions in Ar and propose them as a new benchmark for thermal effects. The developed method is widely applicable for solving the Boltzmann equation that appears in many different contexts in physics., 14 pages

Published
2008

38. Transport in a Dissipative Luttinger Liquid

Author

Thomas Nattermann and Zoran Ristivojevic

Subjects
Physics, Condensed matter physics, Condensed Matter - Mesoscale and Nanoscale Physics, Strongly Correlated Electrons (cond-mat.str-el), General Physics and Astronomy, Conductance, Perturbation (astronomy), FOS: Physical sciences, Dissipation, Condensed Matter::Mesoscopic Systems and Quantum Hall Effect, Condensed Matter - Strongly Correlated Electrons, Luttinger liquid, Impurity, Condensed Matter::Superconductivity, Mesoscale and Nanoscale Physics (cond-mat.mes-hall), Compressibility, Dissipative system, Condensed Matter::Strongly Correlated Electrons, Ohmic contact
Abstract

We study theoretically the transport through a single impurity in a one-channel Luttinger liquid coupled to a dissipative (ohmic) bath . For non-zero dissipation $\eta$ the weak link is always a relevant perturbation which suppresses transport strongly. At zero temperature the current voltage relation of the link is $I\sim \exp(-E_0/eV)$ where $E_0\sim\eta/\kappa$ and $\kappa$ denotes the compressibility. At non-zero temperature $T$ the linear conductance is proportional to $\exp(-\sqrt{{\cal C}E_0/k_BT})$. The decay of Friedel oscillation saturates for distance larger than $L_{\eta}\sim 1/\eta $ from the impurity., Comment: 4 pages

Published
2008
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39. Absence of the Mott Glass Phase in 1D Disordered Fermionic Systems

Author

Friedmar Schütze, Aleksandra Petković, Zoran Ristivojevic, and Thomas Nattermann

Subjects
Physics, Range (particle radiation), Instanton, Condensed matter physics, General Physics and Astronomy, Condensed Matter::Disordered Systems and Neural Networks, 01 natural sciences, Displacement (vector), 010305 fluids & plasmas, Surface tension, Phase (matter), 0103 physical sciences, Compressibility, Strong coupling, Condensed Matter::Strongly Correlated Electrons, 010306 general physics, Phase diagram
Abstract

We study the competition between the Mott and the Anderson insulating state in a one-dimensional disordered fermionic system. The notorious difficulties associated with strong coupling phases are avoided by using a new description in terms of the kink energies (or instanton surface tension) of the electronic displacement pattern. The approach has some similarities to the description of the flat phase of surfaces undergoing a roughening transition. Tracing back both a finite compressibility and a nonzero ac conductivity to vanishing kink energy we exclude the existence of an intermediate Mott-glass phase in systems with short range interaction only. In systems with long range interaction the Anderson insulating phase exhibits the features of a Mott glass however. The phase diagram is constructed from combining the information from the renormalization group flow, the kink energy, and simple rescaling analysis.

Published
2007

40. Fluctuations and entanglement spectrum in quantum Hall states

Author

Karyn Le Hur, H. Francis Song, Stephan Rachel, Alexandru Petrescu, Christian Flindt, Israel Klich, Zoran Ristivojevic, Nicolas Laflorencie, Nicolas Regnault, Fermions Fortement Corrélés (LPT) (FFC), Laboratoire de Physique Théorique (LPT), Institut de Recherche sur les Systèmes Atomiques et Moléculaires Complexes (IRSAMC), Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche sur les Systèmes Atomiques et Moléculaires Complexes (IRSAMC), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Centre de Physique Théorique [Palaiseau] (CPHT), Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X), Département de Physique Théorique, University of Geneva [Switzerland], Laboratoire Pierre Aigrain (LPA), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Fédération de recherche du Département de physique de l'Ecole Normale Supérieure - ENS Paris (FRDPENS), Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Centre National de la Recherche Scientifique (CNRS), Université de Toulouse (UT)-Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche sur les Systèmes Atomiques et Moléculaires Complexes (IRSAMC), Université de Toulouse (UT)-Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS), École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS), Université de Genève = University of Geneva (UNIGE), Fédération de recherche du Département de physique de l'Ecole Normale Supérieure - ENS Paris (FRDPENS), École normale supérieure - Paris (ENS-PSL), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Statistics and Probability, Quantum point contact, FOS: Physical sciences, Quantum entanglement, Quantum Hall effect, 01 natural sciences, 010305 fluids & plasmas, Condensed Matter - Strongly Correlated Electrons, [PHYS.QPHY]Physics [physics]/Quantum Physics [quant-ph], Luttinger liquid, Quantum mechanics, Mesoscale and Nanoscale Physics (cond-mat.mes-hall), 0103 physical sciences, Edge states, 010306 general physics, Entropy (arrow of time), Physics, Quantum Physics, Strongly Correlated Electrons (cond-mat.str-el), Condensed Matter - Mesoscale and Nanoscale Physics, Statistical and Nonlinear Physics, Fermion, [PHYS.COND.CM-GEN]Physics [physics]/Condensed Matter [cond-mat]/Other [cond-mat.other], Bipartite graph, Statistics, Probability and Uncertainty, Quantum Physics (quant-ph)
Abstract

The measurement of quantum entanglement in many-body systems remains challenging. One experimentally relevant fact about quantum entanglement is that in systems whose degrees of freedom map to free fermions with conserved total particle number, exact relations hold relating the Full Counting Statistics associated with the bipartite charge fluctuations and the sequence of R\' enyi entropies. We draw a correspondence between the bipartite charge fluctuations and the entanglement spectrum, mediated by the R\' enyi entropies. In the case of the integer quantum Hall effect, we show that it is possible to reproduce the generic features of the entanglement spectrum from a measurement of the second charge cumulant only. Additionally, asking whether it is possible to extend the free fermion result to the $\nu=1/3$ fractional quantum Hall case, we provide numerical evidence that the answer is negative in general. We further address the problem of quantum Hall edge states described by a Luttinger liquid, and derive expressions for the spectral functions of the real space entanglement spectrum at a quantum point contact realized in a quantum Hall sample., Comment: Final Version. Invited Article, for Special Issue of JSTAT on "Quantum Entanglement in Condensed Matter Physics"

Published
2014

41. Spatial profiles of electron swarm properties and explanation of negative mobility of electrons

Author

Zoran Raspopovic, Anatoly P. Napartovich, Zoran Ristivojevic, Milovan Šuvakov, Z. Lj. Petrović, Sasa Dujko, and Nikolay Dyatko

Subjects
Physics, Nuclear and High Energy Physics, Electron mobility, Electrical mobility, Electric field, Direct current, Electromagnetic electron wave, Radio frequency, Electron, Plasma, Atomic physics, Condensed Matter Physics
Abstract

In this paper, we explain the difference in sign of the flux and bulk drift velocities of a swarm of electrons in constant direct current (dc) and in radio frequency (RF) electric fields under conditions which lead to negative absolute mobility. We have studied (0.5%) F/sub 2//Ar decaying plasma. It was shown that there is a spatial separation of groups of electrons with high and low energy and as a result there is a localization of electron attachment in the region of low energy. Finally, we show that the positive value of the bulk mobility and its delay in RF fields may be explained by a wave of localized attachment that changes the center of mass of the electron swarm.

Published
2005

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