Search

Your search keyword '"Ignacio García-Mata"' showing total 46 results
Start Over Author "Ignacio García-Mata"
46 results on '"Ignacio García-Mata"'

1. Effective versus Floquet theory for the Kerr parametric oscillator

Author

Ignacio García-Mata, Rodrigo G. Cortiñas, Xu Xiao, Jorge Chávez-Carlos, Victor S. Batista, Lea F. Santos, and Diego A. Wisniacki

Subjects
Physics, QC1-999
Abstract

Parametric gates and processes engineered from the perspective of the static effective Hamiltonian of a driven system are central to quantum technology. However, the perturbative expansions used to derive static effective models may not be able to efficiently capture all the relevant physics of the original system. In this work, we investigate the conditions for the validity of the usual low-order static effective Hamiltonian used to describe a Kerr oscillator under a squeezing drive. This system is of fundamental and technological interest. In particular, it has been used to stabilize Schrödinger cat states, which have applications for quantum computing. We compare the states and energies of the effective static Hamiltonian with the exact Floquet states and quasi-energies of the driven system and determine the parameter regime where the two descriptions agree. Our work brings to light the physics that is left out by ordinary static effective treatments and that can be explored by state-of-the-art experiments.

Published
2024
Full Text
View/download PDF

2. Impact of chaos on precursors of quantum criticality

Author

Ignacio García-Mata, Eduardo Vergini, and Diego A. Wisniacki

Subjects
Quantum Physics, FOS: Physical sciences, Chaotic Dynamics (nlin.CD), Quantum Physics (quant-ph), Nonlinear Sciences - Chaotic Dynamics
Abstract

Excited-state quantum phase transitions (ESQPTs) are critical phenomena that generate singularities in the spectrum of quantum systems. {For systems with a classical counterpart,} these phenomena have their origin in the classical limit when the separatrix of an unstable periodic orbit divides phase space into different regions. Using a semiclassical theory of wave propagation based on the manifolds of unstable periodic orbits, we describe the quantum states associated with an ESQPT {for the quantum standard map: a paradigmatic example of a kicked quantum system}. {Moreover, we show that finite-size precursors of ESQPTs shrink as chaos increases due to the disturbance of the system. This phenomenon is explained through destructive interference between principal homoclinic orbits}, 6 pages + Supp. Mat. 4+6 Figs. Closest to published version

Published
2021

3. Symmetry Violation of Quantum Multifractality: Gaussian fluctuations versus Algebraic Localization

Author

Bertrand Georgeot, Olivier Giraud, Gabriel Lemarié, A. M. Bilen, Ignacio García-Mata, Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR), Consejo Nacional de Investigaciones Científicas y Técnicas [Buenos Aires] (CONICET)-Facultad de Ciencias Exactas y Naturales [Mar del Plata], Universidad Nacional de Mar del Plata [Mar del Plata] (UNMdP)-Universidad Nacional de Mar del Plata [Mar del Plata] (UNMdP), 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), Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), MajuLab (UMI 3654), National University of Singapore (NUS)-Sorbonne Université (SU), Centre for Quantum Technologies [Singapore] (CQT), National University of Singapore (NUS), 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), MajuLab, National University of Singapore (NUS)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA), ANR-17-EURE-0009,NanoX,Science et Ingénierie à l'Echelle Nano(2017), ANR-17-CE30-0024,COCOA,Contrôle de systèmes complexes d'atomes froids(2017), ANR-19-CE30-0013,GLADYS,De la nature vitreuse des systèmes quantiques désordonnés(2019), and ANR-18-CE30-0017,MANYLOK,Localisation à N corps avec le Kicked Rotor(2018)

Subjects
Physics, Anderson localization, Quantum Physics, Gaussian, FOS: Physical sciences, Disordered Systems and Neural Networks (cond-mat.dis-nn), Multifractal system, Eigenfunction, Condensed Matter - Disordered Systems and Neural Networks, 16. Peace & justice, 01 natural sciences, Symmetry (physics), 010305 fluids & plasmas, symbols.namesake, [PHYS.QPHY]Physics [physics]/Quantum Physics [quant-ph], Quantum state, 0103 physical sciences, symbols, Quantum Physics (quant-ph), 010306 general physics, Random matrix, Quantum, Mathematical physics
Abstract

Quantum multifractality is a fundamental property of systems such as non-interacting disordered systems at an Anderson transition and many-body systems in Hilbert space. Here we discuss the origin of the presence or absence of a fundamental symmetry related to this property. The anomalous multifractal dimension $\Delta_q$ is used to characterize the structure of quantum states in such systems. Although the multifractal symmetry relation \mbox{$\Delta_q=\Delta_{1-q}$} is universally fulfilled in many known systems, recently some important examples have emerged where it does not hold. We show that this is the result of two different mechanisms. The first one was already known and is related to Gaussian fluctuations well described by random matrix theory. The second one, not previously explored, is related to the presence of an algebraically localized envelope. While the effect of Gaussian fluctuations can be removed by coarse graining, the second mechanism is robust to such a procedure. We illustrate the violation of the symmetry due to algebraic localization on two systems of very different nature, a 1D Floquet critical system and a model corresponding to Anderson localization on random graphs., Comment: Closest to published version

Published
2021

4. Signatures of quantum chaos transition in short spin chains

Author

Diego Ariel Wisniacki, Ignacio García-Mata, Rodolfo A. Jalabert, Emiliano M. Fortes, Institut de Physique et Chimie des Matériaux de Strasbourg (IPCMS), Université de Strasbourg (UNISTRA)-Matériaux et nanosciences d'Alsace (FMNGE), Institut de Chimie du CNRS (INC)-Université de Strasbourg (UNISTRA)-Université de Haute-Alsace (UHA) Mulhouse - Colmar (Université de Haute-Alsace (UHA))-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS)-Institut de Chimie du CNRS (INC)-Université de Strasbourg (UNISTRA)-Université de Haute-Alsace (UHA) Mulhouse - Colmar (Université de Haute-Alsace (UHA))-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS)-Centre National de la Recherche Scientifique (CNRS)-Réseau nanophotonique et optique, and Centre National de la Recherche Scientifique (CNRS)-Université de Strasbourg (UNISTRA)-Université de Haute-Alsace (UHA) Mulhouse - Colmar (Université de Haute-Alsace (UHA))-Centre National de la Recherche Scientifique (CNRS)-Université de Strasbourg (UNISTRA)

Subjects
Degrees of freedom (physics and chemistry), FOS: Physical sciences, General Physics and Astronomy, Quantum simulator, 01 natural sciences, 010305 fluids & plasmas, purl.org/becyt/ford/1 [https], symbols.namesake, Chain (algebraic topology), Quantum mechanics, 0103 physical sciences, 010306 general physics, Quantum, Condensed Matter - Statistical Mechanics, Spin-½, Physics, Quantum Physics, Statistical Mechanics (cond-mat.stat-mech), Spins, Hilbert space, Disordered Systems and Neural Networks (cond-mat.dis-nn), purl.org/becyt/ford/1.3 [https], Condensed Matter - Disordered Systems and Neural Networks, Nonlinear Sciences - Chaotic Dynamics, Quantum chaos, [PHYS.PHYS.PHYS-GEN-PH]Physics [physics]/Physics [physics]/General Physics [physics.gen-ph], Condensed Matter - Other Condensed Matter, CHAOS, symbols, Chaotic Dynamics (nlin.CD), Quantum Physics (quant-ph), QUANTUM, Other Condensed Matter (cond-mat.other)
Abstract

The non-integrability of quantum systems, often associated with chaotic behavior, is a concept typically applied to cases with a high-dimensional Hilbert space Among different indicators signaling this behavior, the study of the long-time oscillations of the out-of-time-ordered correlator (OTOC) appears as a versatile tool, that can be adapted to the case of systems with a small number of degrees of freedom. Using such an approach, we consider the oscillations observed after the scrambling time in the measurement of OTOCs of local operators for an Ising spin chain on a nuclear magnetic resonance quantum simulator [J. Li,et al, Phys. Rev. X 7, 031011 (2017)]. We show that the systematic of the OTOC oscillations describes qualitatively well, in a chain with only 4 spins, the integrability-to-chaos transition inherited from the infinite chain., 6+ pages, 5 figures. Comments welcome

Published
2020

5. Multifractality of open quantum systems

Author

Olivier Giraud, Agustín M. Bilen, Bertrand Georgeot, Ignacio García-Mata, Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR), Consejo Nacional de Investigaciones Científicas y Técnicas [Buenos Aires] (CONICET)-Facultad de Ciencias Exactas y Naturales [Mar del Plata], Universidad Nacional de Mar del Plata [Mar del Plata] (UNMdP)-Universidad Nacional de Mar del Plata [Mar del Plata] (UNMdP), Information et Chaos Quantiques (LPT), 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), Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), Centre National de la Recherche Scientifique (CNRS)-Université Paris-Sud - Paris 11 (UP11), 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
Ciencias Físicas, Chaotic, FOS: Physical sciences, Otras Ciencias Físicas, 01 natural sciences, 010305 fluids & plasmas, purl.org/becyt/ford/1 [https], [PHYS.QPHY]Physics [physics]/Quantum Physics [quant-ph], Quantum state, 0103 physical sciences, Quantum system, Ergodic theory, Statistical physics, 010306 general physics, Quantum, Eigenvalues and eigenvectors, Physics, Quantum Physics, Hierarchy (mathematics), Multifractal system, purl.org/becyt/ford/1.3 [https], Nonlinear Sciences - Chaotic Dynamics, MULTIFRACTALITY, Chaotic Dynamics (nlin.CD), Quantum Physics (quant-ph), QUANTUM, CIENCIAS NATURALES Y EXACTAS
Abstract

We study the eigenstates of open maps whose classical dynamics is pseudointegrable and for which the corresponding closed quantum system has multifractal properties. Adapting the existing general framework developed for open chaotic quantum maps, we specify the relationship between the eigenstates and the classical structures, and quantify their multifractality at different scales. Based on this study, we conjecture that quantum states in such systems are distributed according to a hierarchy of classical structures, but are multifractal instead of ergodic at each level of the hierarchy. This is visible for sufficiently long-lived resonance states at scales smaller than the classical structures. Our results can guide experimentalists in order to observe multifractal behavior in open systems., Comment: 16 pages, 12 figures; closest to published version

Published
2019

6. Two critical localization lengths in the Anderson transition on random graphs

Author

Rémy Dubertrand, John Martin, Olivier Giraud, Ignacio García-Mata, Gabriel Lemarié, Bertrand Georgeot, Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR), Consejo Nacional de Investigaciones Científicas y Técnicas [Buenos Aires] (CONICET)-Facultad de Ciencias Exactas y Naturales [Mar del Plata], Universidad Nacional de Mar del Plata [Mar del Plata] (UNMdP)-Universidad Nacional de Mar del Plata [Mar del Plata] (UNMdP), Institut de Physique Nucléaire, Atomique et de Spectroscopie, CESAM, Université de Liège, Bât. B15, B - 4000 Liège, Institut für Theoretische Physik [Regensburg], Universität Regensburg (UR), Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), Centre National de la Recherche Scientifique (CNRS)-Université Paris-Sud - Paris 11 (UP11), Information et Chaos Quantiques (LPT), 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, 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), and Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)

Subjects
FOS: Physical sciences, 01 natural sciences, 010305 fluids & plasmas, purl.org/becyt/ford/1 [https], [PHYS.QPHY]Physics [physics]/Quantum Physics [quant-ph], 0103 physical sciences, [PHYS.COND]Physics [physics]/Condensed Matter [cond-mat], 010306 general physics, Condensed Matter - Statistical Mechanics, Mathematical physics, Random graph, Physics, G100, Quantum Physics, Statistical Mechanics (cond-mat.stat-mech), LOCALIZATION, Observable, purl.org/becyt/ford/1.3 [https], Disordered Systems and Neural Networks (cond-mat.dis-nn), Renormalization group, Condensed Matter - Disordered Systems and Neural Networks, RANDOM, GRAPH, Quantum Physics (quant-ph), QUANTUM, Critical exponent
Abstract

We present a full description of the nonergodic properties of wavefunctions on random graphs without boundary in the localized and critical regimes of the Anderson transition. We find that they are characterized by two critical localization lengths: the largest one describes localization along rare branches and diverges with a critical exponent $\nu_\parallel=1$ at the transition. The second length, which describes localization along typical branches, reaches at the transition a finite universal value (which depends only on the connectivity of the graph), with a singularity controlled by a new critical exponent $\nu_\perp=1/2$. We show numerically that these two localization lengths control the finite-size scaling properties of key observables: wavefunction moments, correlation functions and spectral statistics. Our results are identical to the theoretical predictions for the typical localization length in the many-body localization transition, with the same critical exponent. This strongly suggests that the two transitions are in the same universality class and that our techniques could be directly applied in this context., Comment: 6 pages, 3 figures; Corresponds to the published version

Published
2019

7. Gauging classical and quantum integrability through out-of-time ordered correlators

Author

Diego Ariel Wisniacki, Emiliano M. Fortes, Ignacio García-Mata, Rodolfo A. Jalabert, Institut de Physique et Chimie des Matériaux de Strasbourg (IPCMS), Université de Strasbourg (UNISTRA)-Matériaux et nanosciences d'Alsace, Université de Strasbourg (UNISTRA)-Université de Haute-Alsace (UHA) Mulhouse - Colmar (Université de Haute-Alsace (UHA))-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS)-Université de Strasbourg (UNISTRA)-Université de Haute-Alsace (UHA) Mulhouse - Colmar (Université de Haute-Alsace (UHA))-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS)-Centre National de la Recherche Scientifique (CNRS)-Réseau nanophotonique et optique, Université de Strasbourg (UNISTRA)-Université de Haute-Alsace (UHA) Mulhouse - Colmar (Université de Haute-Alsace (UHA))-Centre National de la Recherche Scientifique (CNRS)-Université de Strasbourg (UNISTRA), Université de Strasbourg (UNISTRA)-Matériaux et nanosciences d'Alsace (FMNGE), Institut de Chimie du CNRS (INC)-Université de Strasbourg (UNISTRA)-Université de Haute-Alsace (UHA) Mulhouse - Colmar (Université de Haute-Alsace (UHA))-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS)-Institut de Chimie du CNRS (INC)-Université de Strasbourg (UNISTRA)-Université de Haute-Alsace (UHA) Mulhouse - Colmar (Université de Haute-Alsace (UHA))-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS)-Centre National de la Recherche Scientifique (CNRS)-Réseau nanophotonique et optique, and Centre National de la Recherche Scientifique (CNRS)-Université de Strasbourg (UNISTRA)-Université de Haute-Alsace (UHA) Mulhouse - Colmar (Université de Haute-Alsace (UHA))-Centre National de la Recherche Scientifique (CNRS)-Université de Strasbourg (UNISTRA)

Subjects
Ciencias Físicas, Chaotic, FOS: Physical sciences, Otras Ciencias Físicas, 01 natural sciences, Nonlinear Dynamics and Chaos, Classical limit, 010305 fluids & plasmas, purl.org/becyt/ford/1 [https], 0103 physical sciences, Statistical physics, 010306 general physics, Quantum, Eigenvalues and eigenvectors, Spin-½, Physics, Quantum Physics, Basis (linear algebra), purl.org/becyt/ford/1.3 [https], Gauge (firearms), Nonlinear Sciences - Chaotic Dynamics, Quantum chaos, [PHYS.PHYS.PHYS-GEN-PH]Physics [physics]/Physics [physics]/General Physics [physics.gen-ph], CHAOS, Chaotic Dynamics (nlin.CD), Quantum Physics (quant-ph), QUANTUM, CIENCIAS NATURALES Y EXACTAS
Abstract

Out-of-time-order correlators (OTOCs) have been proposed as a probe of chaos in quantum mechanics, on the basis of their short-time exponential growth found in some particular set-ups. However, it has been seen that this behavior is not universal. Therefore, we query other quantum chaos manifestations arising from the OTOCs and we thus study their long-time behavior in systems of completely different nature: quantum maps, which are the simplest chaotic one-body system and spin chains, which are many-body systems without a classical limit. It is shown that studying the long-time regime of the OTOCs it is possible to detect and gauge the transition between integrability and chaos, and we benchmark the transition with other indicators of quantum chaos based on the spectra and the eigenstates of the systems considered. For systems with classical analogue, we show that the proposed OTOC indicators have a very high accuracy that allow to detect subtle features along the integrability-to-chaos transition., Comment: Closest to published version. Included changes suggested by referees, grammar changes according to editors, enhanced quality and resolution of figures, etc

Published
2019
Full Text
View/download PDF

8. Semiclassical theory of out-of-time-order correlators for low-dimensional classically chaotic systems

Author

Diego Ariel Wisniacki, Rodolfo A. Jalabert, Ignacio García-Mata, Institut de Physique et Chimie des Matériaux de Strasbourg (IPCMS), Université de Strasbourg (UNISTRA)-Matériaux et nanosciences d'Alsace, Université de Strasbourg (UNISTRA)-Université de Haute-Alsace (UHA) Mulhouse - Colmar (Université de Haute-Alsace (UHA))-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS)-Université de Strasbourg (UNISTRA)-Université de Haute-Alsace (UHA) Mulhouse - Colmar (Université de Haute-Alsace (UHA))-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS)-Centre National de la Recherche Scientifique (CNRS)-Réseau nanophotonique et optique, Université de Strasbourg (UNISTRA)-Université de Haute-Alsace (UHA) Mulhouse - Colmar (Université de Haute-Alsace (UHA))-Centre National de la Recherche Scientifique (CNRS)-Université de Strasbourg (UNISTRA), Université de Strasbourg (UNISTRA)-Matériaux et nanosciences d'Alsace (FMNGE), Institut de Chimie du CNRS (INC)-Université de Strasbourg (UNISTRA)-Université de Haute-Alsace (UHA) Mulhouse - Colmar (Université de Haute-Alsace (UHA))-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS)-Institut de Chimie du CNRS (INC)-Université de Strasbourg (UNISTRA)-Université de Haute-Alsace (UHA) Mulhouse - Colmar (Université de Haute-Alsace (UHA))-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS)-Centre National de la Recherche Scientifique (CNRS)-Réseau nanophotonique et optique, Centre National de la Recherche Scientifique (CNRS)-Université de Strasbourg (UNISTRA)-Université de Haute-Alsace (UHA) Mulhouse - Colmar (Université de Haute-Alsace (UHA))-Centre National de la Recherche Scientifique (CNRS)-Université de Strasbourg (UNISTRA), Université de Strasbourg (UNISTRA)-Centre National de la Recherche Scientifique (CNRS)-Matériaux et nanosciences d'Alsace (FMNGE), and Institut de Chimie du CNRS (INC)-Université de Strasbourg (UNISTRA)-Université de Haute-Alsace (UHA) Mulhouse - Colmar (Université de Haute-Alsace (UHA))-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS)-Institut de Chimie du CNRS (INC)-Université de Strasbourg (UNISTRA)-Université de Haute-Alsace (UHA) Mulhouse - Colmar (Université de Haute-Alsace (UHA))-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS)-Réseau nanophotonique et optique

Subjects
Ciencias Físicas, FOS: Physical sciences, Semiclassical physics, Lyapunov exponent, Otras Ciencias Físicas, 01 natural sciences, Nonlinear Dynamics and Chaos, 010305 fluids & plasmas, purl.org/becyt/ford/1 [https], symbols.namesake, Chaotic systems, 0103 physical sciences, Statistical physics, 010306 general physics, Quantum, Physics, Quantum Physics, Order (ring theory), purl.org/becyt/ford/1.3 [https], Nonlinear Sciences - Chaotic Dynamics, [PHYS.PHYS.PHYS-GEN-PH]Physics [physics]/Physics [physics]/General Physics [physics.gen-ph], Nonlinear Sciences::Chaotic Dynamics, Condensed Matter - Other Condensed Matter, CHAOS, symbols, Chaotic Dynamics (nlin.CD), Quantum Physics (quant-ph), QUANTUM, CIENCIAS NATURALES Y EXACTAS, Other Condensed Matter (cond-mat.other)
Abstract

The out-of-time-order correlator (OTOC), recently analyzed in several physical contexts, is studied for low-dimensional chaotic systems through semiclassical expansions and numerical simulations. The semiclassical expansion for the OTOC yields a leading-order contribution in $\hbar^2$ that is exponentially increasing with time within an intermediate, temperature-dependent, time-window. The growth-rate in such a regime is governed by the Lyapunov exponent of the underlying classical system and scales with the square-root of the temperature., 24 pages (one column), 7 figures. Some changes and corrections added. Closest to published version

Published
2018

9. Chaos signatures in the short and long time behavior of the out-of-time ordered correlator

Author

Ignacio García-Mata, Augusto J. Roncaglia, Rodolfo A. Jalabert, Marcos Saraceno, Diego Ariel Wisniacki, Institut de Physique et Chimie des Matériaux de Strasbourg (IPCMS), Université de Strasbourg (UNISTRA)-Matériaux et nanosciences d'Alsace (FMNGE), Institut de Chimie du CNRS (INC)-Université de Strasbourg (UNISTRA)-Université de Haute-Alsace (UHA) Mulhouse - Colmar (Université de Haute-Alsace (UHA))-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS)-Institut de Chimie du CNRS (INC)-Université de Strasbourg (UNISTRA)-Université de Haute-Alsace (UHA) Mulhouse - Colmar (Université de Haute-Alsace (UHA))-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS)-Centre National de la Recherche Scientifique (CNRS)-Réseau nanophotonique et optique, Centre National de la Recherche Scientifique (CNRS)-Université de Strasbourg (UNISTRA)-Université de Haute-Alsace (UHA) Mulhouse - Colmar (Université de Haute-Alsace (UHA))-Centre National de la Recherche Scientifique (CNRS)-Université de Strasbourg (UNISTRA), Université de Strasbourg (UNISTRA)-Centre National de la Recherche Scientifique (CNRS)-Matériaux et nanosciences d'Alsace, Université de Strasbourg (UNISTRA)-Université de Haute-Alsace (UHA) Mulhouse - Colmar (Université de Haute-Alsace (UHA))-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS)-Université de Strasbourg (UNISTRA)-Université de Haute-Alsace (UHA) Mulhouse - Colmar (Université de Haute-Alsace (UHA))-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS)-Réseau nanophotonique et optique, and Université de Strasbourg (UNISTRA)-Université de Haute-Alsace (UHA) Mulhouse - Colmar (Université de Haute-Alsace (UHA))-Centre National de la Recherche Scientifique (CNRS)-Université de Strasbourg (UNISTRA)

Subjects
Física Atómica, Molecular y Química, Ciencias Físicas, Chaotic, Physical system, General Physics and Astronomy, FOS: Physical sciences, Lyapunov exponent, 01 natural sciences, Measure (mathematics), 010305 fluids & plasmas, purl.org/becyt/ford/1 [https], symbols.namesake, 0103 physical sciences, Statistical physics, 010306 general physics, Quantum, Mixing (physics), Physics, Quantum Physics, etc, General Physics: Statistical and Quantum Mechanics, purl.org/becyt/ford/1.3 [https], 16. Peace & justice, Nonlinear Sciences - Chaotic Dynamics, Quantum chaos, Out of time order operators, [PHYS.PHYS.PHYS-GEN-PH]Physics [physics]/Physics [physics]/General Physics [physics.gen-ph], Exponential function, quantum maps, Nonlinear Sciences::Chaotic Dynamics, symbols, Quantum Information, Chaotic Dynamics (nlin.CD), Quantum Physics (quant-ph), CIENCIAS NATURALES Y EXACTAS, quantum chaos
Abstract

Two properties are needed for a classical system to be chaotic: exponential stretching and mixing. Recently, out-of-time order correlators were proposed as a measure of chaos in a wide range of physical systems. While most of the attention has previously been devoted to the short time stretching aspect of chaos, characterized by the Lyapunov exponent, we show for quantum maps that the out-of-time correlator approaches its stationary value exponentially with a rate determined by the Ruelle-Pollicot resonances. This property constitutes clear evidence of the dual role of the underlying classical chaos dictating the behavior of the correlator at different timescales., Comment: 4+1/2 pages + small appendix -- Closest to published version [minor typo in Eq. (5) corrected]

Published
2018

10. Quantum-to-classical transition in the work distribution for chaotic systems

Author

Ignacio García-Mata, Augusto J. Roncaglia, and Diego Ariel Wisniacki

Subjects
Dephasing, Ciencias Físicas, Chaotic, Non-equilibrium thermodynamics, Semiclassical physics, FOS: Physical sciences, 01 natural sciences, 010305 fluids & plasmas, purl.org/becyt/ford/1 [https], symbols.namesake, 0103 physical sciences, THERMODYNAMICS, Wigner distribution function, 010306 general physics, Quantum, Physics, Quantum Physics, purl.org/becyt/ford/1.3 [https], Nonlinear Sciences - Chaotic Dynamics, Nonlinear Sciences::Chaotic Dynamics, Astronomía, Classical mechanics, symbols, Quantum ergodicity, Chaotic Dynamics (nlin.CD), Hamiltonian (quantum mechanics), Quantum Physics (quant-ph), QUANTUM, CIENCIAS NATURALES Y EXACTAS
Abstract

The work distribution is a fundamental quantity in nonequilibrium thermodynamics mainly due to its connection with fluctuations theorems. Here we develop a semiclassical approximation to the work distribution for a quench process in chaotic systems. The approach is based on the dephasing representation of the quantum Loschmidt echo and on the quantum ergodic conjecture, which states that the Wigner function of a typical eigenstate of a classically chaotic Hamiltonian is equidistributed on the energy shell. We show that our semiclassical approximation is accurate in describing the quantum distribution as we increase the temperature. Moreover, we also show that this semiclassical approximation provides a link between the quantum and classical work distributions., Comment: 4+ pages, 4 figures. 2+ pages Sup. Mat

Published
2017

11. Scaling Theory of the Anderson Transition in Random Graphs: Ergodicity and Universality

Author

Ignacio García-Mata, Olivier Giraud, Rémy Dubertrand, John Martin, Bertrand Georgeot, Gabriel Lemarié, Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR), Consejo Nacional de Investigaciones Científicas y Técnicas [Buenos Aires] (CONICET)-Facultad de Ciencias Exactas y Naturales [Mar del Plata], Universidad Nacional de Mar del Plata [Mar del Plata] (UNMdP)-Universidad Nacional de Mar del Plata [Mar del Plata] (UNMdP), Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), Centre National de la Recherche Scientifique (CNRS)-Université Paris-Sud - Paris 11 (UP11), Information et Chaos Quantiques (LPT), 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 de Physique Nucl'eaire, Atomique et de Spectroscopie, Université de Liège, 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), and Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)

Subjects
Anderson localization, F300, Ciencias Físicas, Physics::Optics, FOS: Physical sciences, General Physics and Astronomy, Condensed Matter::Disordered Systems and Neural Networks, 01 natural sciences, GRAPHS, 010305 fluids & plasmas, purl.org/becyt/ford/1 [https], Delocalized electron, 0103 physical sciences, FOS: Mathematics, Ergodic theory, [PHYS.COND.CM-DS-NN]Physics [physics]/Condensed Matter [cond-mat]/Disordered Systems and Neural Networks [cond-mat.dis-nn], Statistical physics, [PHYS.COND.CM-SM]Physics [physics]/Condensed Matter [cond-mat]/Statistical Mechanics [cond-mat.stat-mech], 010306 general physics, Scaling, Condensed Matter - Statistical Mechanics, random graphs, Condensed Matter::Quantum Gases, Random graph, Physics, Quantum Physics, COMPLEX, Statistical Mechanics (cond-mat.stat-mech), Condensed matter physics, ddc:530, Probability (math.PR), Ergodicity, transition, LOCALIZATION, purl.org/becyt/ford/1.3 [https], Disordered Systems and Neural Networks (cond-mat.dis-nn), Multifractal system, Condensed Matter - Disordered Systems and Neural Networks, 530 Physik, Universality (dynamical systems), Astronomía, [NLIN.NLIN-CD]Nonlinear Sciences [physics]/Chaotic Dynamics [nlin.CD], ergodicity, Condensed Matter::Strongly Correlated Electrons, Quantum Physics (quant-ph), QUANTUM, Mathematics - Probability, CIENCIAS NATURALES Y EXACTAS
Abstract

We study the Anderson transition on a generic model of random graphs with a tunable branching parameter $1, Comment: 5+5 pages, 4+4 figures

Published
2017
Full Text
View/download PDF

12. Semiclassical approach to the work distribution

Author

Augusto J. Roncaglia, Diego Ariel Wisniacki, and Ignacio García-Mata

Subjects
Work (thermodynamics), Distribution (number theory), Ciencias Físicas, Chaotic, Quantum Thermodynamics, General Physics and Astronomy, Semiclassical physics, FOS: Physical sciences, 01 natural sciences, Classical limit, 010305 fluids & plasmas, purl.org/becyt/ford/1 [https], 0103 physical sciences, Quantum work, 010306 general physics, Quantum, Quantum fluctuation, Condensed Matter - Statistical Mechanics, Physics, Quantum Physics, Statistical Mechanics (cond-mat.stat-mech), purl.org/becyt/ford/1.3 [https], Nonlinear Sciences - Chaotic Dynamics, Astronomía, Nonlinear Sciences::Chaotic Dynamics, Classical mechanics, Correspondence principle, Semiclassics, Chaotic Dynamics (nlin.CD), Quantum Physics (quant-ph), CIENCIAS NATURALES Y EXACTAS
Abstract

Work in closed quantum systems is usually defined by a two-point measurement. This definition of work is compatible with quantum fluctuation theorems but it fundamentally differs from its classical counterpart. In this paper, we study the correspondence principle in quantum chaotic systems. We derive a semiclassical expression of the work distribution for chaotic systems undergoing a general, finite time, process. This semiclassical distribution converges to the classical distribution in the usual classical limit. We show numerically that, for a particle inside a chaotic cavity, the semiclassical distribution provides a good approximation to quantum distribution., Comment: 5 pages, 4 figures

Published
2017
Full Text
View/download PDF

13. Average diagonal entropy in nonequilibrium isolated quantum systems

Author

Olivier Giraud, Ignacio García-Mata, Le Vaou, Claudine, Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), Centre National de la Recherche Scientifique (CNRS)-Université Paris-Sud - Paris 11 (UP11), Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR), Consejo Nacional de Investigaciones Científicas y Técnicas [Buenos Aires] (CONICET)-Facultad de Ciencias Exactas y Naturales [Mar del Plata], and Universidad Nacional de Mar del Plata [Mar del Plata] (UNMdP)-Universidad Nacional de Mar del Plata [Mar del Plata] (UNMdP)

Subjects
Ciencias Físicas, Configuration entropy, FOS: Physical sciences, Strong Subadditivity of Quantum Entropy, 01 natural sciences, [PHYS] Physics [physics], 010305 fluids & plasmas, Generalized relative entropy, purl.org/becyt/ford/1 [https], CUANTICA, Quantum mechanics, 0103 physical sciences, Statistical physics, Entropy (energy dispersal), 010306 general physics, ComputingMilieux_MISCELLANEOUS, Mathematics, [PHYS]Physics [physics], Quantum Physics, Quantum discord, ENTROPIA, Maximum entropy thermodynamics, purl.org/becyt/ford/1.3 [https], Quantum relative entropy, 3. Good health, Astronomía, Quantum Physics (quant-ph), Joint quantum entropy, CIENCIAS NATURALES Y EXACTAS
Abstract

The diagonal entropy was introduced as a good entropy candidate especially for isolated quantum systems out of equilibrium. Here we present an analytical calculation of the average diagonal entropy for systems undergoing unitary evolution and an external perturbation in the form of a cyclic quench. We compare our analytical findings with numerical simulations of various many-body quantum systems. Our calculations elucidate various heuristic relations proposed recently in the literature., 5 pages + 4 page "Supplemental material", 2 figures

Published
2016

14. Measuring and using non-Markovianity

Author

Diego Ariel Wisniacki, Carlos Pineda, Thomas Gorin, David Davalos, and Ignacio García-Mata

Subjects
Theoretical computer science, Ciencias Físicas, FOS: Physical sciences, Sistemas, 01 natural sciences, 010305 fluids & plasmas, purl.org/becyt/ford/1 [https], Channel capacity, Resource (project management), 0103 physical sciences, 010306 general physics, Quantum, Physics, Quantum Physics, Cuanticos, purl.org/becyt/ford/1.3 [https], Quantum evolution, Astronomía, Qubit, Quantum process, Quantum Physics (quant-ph), Construct (philosophy), Abiertos, CIENCIAS NATURALES Y EXACTAS, Communication channel
Abstract

We construct measures for the non-Markovianity of quantum evolution with a physically meaningful interpretation. We first provide a general setting in the framework of channel capacities and propose two families of meaningful quantitative measures, based on the largest revival of a channel capacity, avoiding some drawbacks of other non-Markovianity measures. We relate the proposed measures to the task of information screening. This shows that the non-Markovianity of a quantum process may be used as a resource. Under these considerations, we analyze two paradigmatic examples, a qubit in a quantum environment with classically mixed dynamics and the Jaynes-Cummings model., Comment: 9 pages, 6 figures

Published
2016

15. Multifractality of quantum wave functions in the presence of perturbations

Author

Ignacio García-Mata, Rémy Dubertrand, Olivier Giraud, Gabriel Lemarié, Bertrand Georgeot, John Martin, Information et Chaos Quantiques (LPT), 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), Université de Liège, Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR), Consejo Nacional de Investigaciones Científicas y Técnicas [Buenos Aires] (CONICET)-Facultad de Ciencias Exactas y Naturales [Mar del Plata], Universidad Nacional de Mar del Plata [Mar del Plata] (UNMdP)-Universidad Nacional de Mar del Plata [Mar del Plata] (UNMdP), Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), Centre National de la Recherche Scientifique (CNRS)-Université Paris-Sud - Paris 11 (UP11), 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
Characteristic length, F300, Ciencias Físicas, FOS: Physical sciences, Otras Ciencias Físicas, purl.org/becyt/ford/1 [https], Fractal, [PHYS.QPHY]Physics [physics]/Quantum Physics [quant-ph], [NLIN]Nonlinear Sciences [physics], Statistical physics, Localizacion, Wave function, Scaling, Anderson impurity model, Quantum, Mathematics, Quantum Physics, ddc:530, 05.45.Df, 05.45.Mt, 71.30.+h, 05.40.-a, 05.45.Df, 05.45.Mt, 71.30.+h, 05.40.−a, Disordered Systems and Neural Networks (cond-mat.dis-nn), purl.org/becyt/ford/1.3 [https], Condensed Matter - Disordered Systems and Neural Networks, 530 Physik, Nonlinear Sciences - Chaotic Dynamics, Quantum chaos, Cuantica, Chaotic Dynamics (nlin.CD), Quantum Physics (quant-ph), Random matrix, CIENCIAS NATURALES Y EXACTAS
Abstract

We present a comprehensive study of the destruction of quantum multifractality in the presence of perturbations. We study diverse representative models displaying multifractality, including a pseudointegrable system, the Anderson model and a random matrix model. We apply several types of natural perturbations which can be relevant for experimental implementations. We construct an analytical theory for certain cases, and perform extensive large-scale numerical simulations in other cases. The data are analyzed through refined methods including double scaling analysis. Our results confirm the recent conjecture that multifractality breaks down following two scenarios. In the first one, multifractality is preserved unchanged below a certain characteristic length which decreases with perturbation strength. In the second one, multifractality is affected at all scales and disappears uniformly for a strong enough perturbation. Our refined analysis shows that subtle variants of these scenarios can be present in certain cases. This study could guide experimental implementations in order to observe quantum multifractality in real systems., 20 pages, 27 figures

Published
2015

16. Lyapunov decay in quantum irreversibility

Author

Augusto J. Roncaglia, Ignacio García-Mata, and Diego Ariel Wisniacki

Subjects
Lyapunov function, Lyapunov decay, Ciencias Físicas, General Mathematics, General Physics and Astronomy, Perturbation (astronomy), FOS: Physical sciences, Lyapunov exponent, Loschmidt echo, 01 natural sciences, 010305 fluids & plasmas, symbols.namesake, 0103 physical sciences, Statistical physics, 010306 general physics, Quantum, Physics, Quantum Physics, General Engineering, Hilbert space, Articles, Nonlinear Sciences - Chaotic Dynamics, Quantum chaos, Universality (dynamical systems), Astronomía, Nonlinear Sciences::Chaotic Dynamics, irreversibility, symbols, Dynamical billiards, Chaotic Dynamics (nlin.CD), Quantum Physics (quant-ph), CIENCIAS NATURALES Y EXACTAS
Abstract

The Loschmidt echo -- also known as fidelity -- is a very useful tool to study irreversibility in quantum mechanics due to perturbations or imperfections. Many different regimes, as a function of time and strength of the perturbation, have been identified. For chaotic systems, there is a range of perturbation strengths where the decay of the Loschmidt echo is perturbation independent, and given by the classical Lyapunov exponent. But observation of the Lyapunov decay depends strongly on the type of initial state upon which an average is done. This dependence can be removed by averaging the fidelity over the Haar measure, and the Lyapunov regime is recovered, as it was shown for quantum maps. In this work we introduce an analogous quantity for systems with infinite dimensional Hilbert space, in particular the quantum stadium billiard, and we show clearly the universality of the Lyapunov regime., Comment: 8 pages, 6 figures. Accepted in Phil. Trans. R. Soc. A

Published
2015
Full Text
View/download PDF

17. Relaxation of isolated quantum systems beyond chaos

Author

Ignacio García-Mata, Augusto J. Roncaglia, and Diego Ariel Wisniacki

Subjects
Physics, Física Atómica, Molecular y Química, Quantum Physics, Statistical Mechanics (cond-mat.stat-mech), Ciencias Físicas, FOS: Physical sciences, Equilibrio, Cuantico, Thermodinamica, purl.org/becyt/ford/1.3 [https], Nonlinear Sciences - Chaotic Dynamics, purl.org/becyt/ford/1 [https], Nonlinear Sciences::Chaotic Dynamics, Quantum mechanics, Caos, Chaotic Dynamics (nlin.CD), Quantum Physics (quant-ph), Humanities, CIENCIAS NATURALES Y EXACTAS, Condensed Matter - Statistical Mechanics
Abstract

In classical statistical mechanics there is a clear correlation between relaxation to equilibrium and chaos. In contrast, for isolated quantum systems this relation is -- to say the least -- fuzzy. In this work we try to unveil the intricate relation between the relaxation process and the transition from integrability to chaos. We study the approach to equilibrium in two different many body quantum systems that can be parametrically tuned from regular to chaotic. We show that a universal relation between relaxation and delocalization of the initial state in the perturbed basis can be established regardless of the chaotic nature of system., 4+ pages, 4 figs. Closest to published version

Published
2014

18. Two scenarios for quantum multifractality breakdown

Author

Ignacio García-Mata, Bertrand Georgeot, Gabriel Lemarié, John Martin, Olivier Giraud, Rémy Dubertrand, Information et Chaos Quantiques (LPT), 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, Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR), Consejo Nacional de Investigaciones Científicas y Técnicas [Buenos Aires] (CONICET)-Facultad de Ciencias Exactas y Naturales [Mar del Plata], Universidad Nacional de Mar del Plata [Mar del Plata] (UNMdP)-Universidad Nacional de Mar del Plata [Mar del Plata] (UNMdP), Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), Centre National de la Recherche Scientifique (CNRS)-Université Paris-Sud - Paris 11 (UP11), Institut de Physique Nucléaire, Atomique et de Spectroscopie, Université de Liège, 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), and Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)

Subjects
METAL-AISLANTE, F300, Ciencias Físicas, General Physics and Astronomy, Perturbation (astronomy), FOS: Physical sciences, Otras Ciencias Físicas, purl.org/becyt/ford/1 [https], RUIDO, Fractal, [PHYS.QPHY]Physics [physics]/Quantum Physics [quant-ph], TRANSICION, Ergodic theory, Statistical physics, Quantum, Anderson impurity model, Quantum fluctuation, Physics, Quantum Physics, purl.org/becyt/ford/1.3 [https], Multifractal system, Disordered Systems and Neural Networks (cond-mat.dis-nn), Condensed Matter - Disordered Systems and Neural Networks, Nonlinear Sciences - Chaotic Dynamics, Quantum chaos, [PHYS.COND.CM-GEN]Physics [physics]/Condensed Matter [cond-mat]/Other [cond-mat.other], [NLIN.NLIN-CD]Nonlinear Sciences [physics]/Chaotic Dynamics [nlin.CD], CHAOS, Chaotic Dynamics (nlin.CD), Quantum Physics (quant-ph), CIENCIAS NATURALES Y EXACTAS
Abstract

We expose two scenarios for the breakdown of quantum multifractality under the effect of perturbations. In the first scenario, multifractality survives below a certain scale of the quantum fluctuations. In the other one, the fluctuations of the wave functions are changed at every scale and each multifractal dimension smoothly goes to the ergodic value. We use as generic examples a one-dimensional dynamical system and the three-dimensional Anderson model at the metal-insulator transition. Based on our results, we conjecture that the sensitivity of quantum multifractality to perturbation is universal in the sense that it follows one of these two scenarios depending on the perturbation. We also discuss the experimental implications., Comment: 5 pages, 4 figures, minor modifications, published version

Published
2014

19. Comment on 'Exploring chaos in the Dicke model using ground-state fidelity and the Loschmidt echo'

Author

Augusto J. Roncaglia, Ignacio García-Mata, and Diego Ariel Wisniacki

Subjects
Quantum phase transition, Physics, Quantum Physics, media_common.quotation_subject, Fidelity, FOS: Physical sciences, Parity (physics), Quantum chaos, Coupling parameter, Quantum mechanics, Quantum information, Ground state, Quantum Physics (quant-ph), media_common
Abstract

In [PRE \textbf{90}, 022920 (2014), arXiv:1404.6738] a study of the ground state fidelity of the Dicke model as a function of the coupling parameter is presented. Abrupt jumps of the fidelity in the superradiant phase are observed and are assumed to be related to the transition to chaos. We show that this conclusion results from a misinterpretation of the numerics. In fact, if the parity symmetry is taken into account, the unexpected jumps disappear.

Published
2014
Full Text
View/download PDF

20. Quantum non-Markovian behavior at the chaos border

Author

Carlos Pineda, Ignacio García-Mata, and Diego Ariel Wisniacki

Subjects
Statistics and Probability, SEMICLASICOS, Integrable system, Ciencias Físicas, Chaotic, FOS: Physical sciences, General Physics and Astronomy, Otras Ciencias Físicas, METODOS, Statistical physics, Quantum, Mathematical Physics, Physics, Quantum Physics, Phase portrait, CUANTICO, Statistical and Nonlinear Physics, Function (mathematics), Nonlinear Sciences - Chaotic Dynamics, Modeling and Simulation, Phase space, Qubit, CAOS, Chaotic Dynamics (nlin.CD), Quantum Physics (quant-ph), Maxima, CIENCIAS NATURALES Y EXACTAS
Abstract

In this work we study the non-Markovian behaviour of a qubit coupled to an environment in which the corresponding classical dynamics change from integrable to chaotic. We show that in the transition region, where the dynamics has both regular islands and chaotic areas, the average non-Markovian behaviour is enhanced to values even larger than in the regular regime. This effect can be related to the non-Markovian behaviour as a function of the the initial state of the environment, where maxima are attained at the regions dividing separate areas in classical phase space, particularly at the borders between chaotic and regular regions. Moreover, we show that the fluctuations of the fidelity of the environment -- which determine the non-Markovianity measure -- give a precise image of the classical phase portrait., 23 pages, 9 figures (JPA style). Closest to published version

Published
2014

21. The photon-box Bohr-Einstein debate demythologized

Author

Ignacio García-Mata, A. Daleo, and A. C. de la Torre

Subjects
Condensed Matter::Quantum Gases, Physics, General Relativity and Quantum Cosmology, Theoretical physics, symbols.namesake, Photon, Argument, symbols, General Physics and Astronomy, Einstein, Physics::History of Physics, Bohr model
Abstract

The legendary discussion between Einstein and Bohr concerning the photon-box experiment is critically analysed. It is shown that Einstein's argument is flawed while Bohr's reply is wrong.

Published
2000

22. Non-Markovian Quantum Dynamics and Classical Chaos

Author

Carlos Pineda, Ignacio García-Mata, and Diego Ariel Wisniacki

Subjects
Physics, Control of chaos, Quantum Physics, Quantum decoherence, Quantum dynamics, Synchronization of chaos, Measure (physics), FOS: Physical sciences, Nonlinear Sciences - Chaotic Dynamics, Atomic and Molecular Physics, and Optics, Quantum chaos, Open quantum system, Classical mechanics, Sensitivity (control systems), Chaotic Dynamics (nlin.CD), Quantum Physics (quant-ph)
Abstract

We study the influence of a chaotic environment in the evolution of an open quantum system. We show that there is an inverse relation between chaos and non-Markovianity. In particular, we remark on the deep relation of the short time non-Markovian behavior with the revivals of the average fidelity amplitude-a fundamental quantity used to measure sensitivity to perturbations and to identify quantum chaos. The long time behavior is established as a finite size effect which vanishes for large enough environments., Closest to the published version

Published
2012

23. Multifractality of quantum wave packets

Author

Olivier Giraud, Bertrand Georgeot, Ignacio García-Mata, John Martin, Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR), Consejo Nacional de Investigaciones Científicas y Técnicas [Buenos Aires] (CONICET)-Facultad de Ciencias Exactas y Naturales [Mar del Plata], Universidad Nacional de Mar del Plata [Mar del Plata] (UNMdP)-Universidad Nacional de Mar del Plata [Mar del Plata] (UNMdP), Information et Chaos Quantiques (LPT), 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), Institut de Physique Nucl'eaire, Atomique et de Spectroscopie, Université de Liège, Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), Centre National de la Recherche Scientifique (CNRS)-Université Paris-Sud - Paris 11 (UP11), 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
Wave packet, Measure (physics), FOS: Physical sciences, Physics::Data Analysis, Statistics and Probability, 01 natural sciences, 010305 fluids & plasmas, Fractal, 0103 physical sciences, Computer Simulation, Statistical physics, Limit (mathematics), 010306 general physics, Quantum, Eigenvalues and eigenvectors, Physics, Quantum Physics, Disordered Systems and Neural Networks (cond-mat.dis-nn), Models, Theoretical, Condensed Matter - Disordered Systems and Neural Networks, Nonlinear Sciences - Chaotic Dynamics, Quantum chaos, Fractals, [PHYS.COND.CM-GEN]Physics [physics]/Condensed Matter [cond-mat]/Other [cond-mat.other], [NLIN.NLIN-CD]Nonlinear Sciences [physics]/Chaotic Dynamics [nlin.CD], Quantum Theory, Chaotic Dynamics (nlin.CD), Quantum Physics (quant-ph)
Abstract

We study a version of the mathematical Ruijsenaars-Schneider model, and reinterpret it physically in order to describe the spreading with time of quantum wave packets in a system where multifractality can be tuned by varying a parameter. We compare different methods to measure the multifractality of wave packets, and identify the best one. We find the multifractality to decrease with time until it reaches an asymptotic limit, different from the mulifractality of eigenvectors, but related to it, as is the rate of the decrease. Our results could guide the study of experimental situations where multifractality is present in quantum systems., Comment: 6 pages, 4 figures, final version including a new figure (figure 1)

Published
2012
Full Text
View/download PDF

24. Non-Markovian Behavior of Small and Large Complex Quantum Systems

Author

Marko Žnidarič, Carlos Pineda, and Ignacio García-Mata

Subjects
Physics, Quantum Physics, Quantum discord, Quantum dynamics, FOS: Physical sciences, General Physics and Astronomy, Quantum capacity, Quantum channel, Open quantum system, Classical mechanics, Qubit, Quantum Physics (quant-ph), Quantum dissipation, Amplitude damping channel
Abstract

The channel induced by a complex system interacting strongly with a qubit is calculated exactly under the assumption of randomness of its eigenvectors. The resulting channel is represented as an isotropic time dependent oscillation of the Bloch ball, leading to non-Markovian behavior, even in the limit of infinite environments. Two contributions are identified: one due to the density of states and the other due to correlations in the spectrum. Prototype examples, one for chaotic and the other for regular dynamics are explored., 7 pages, 4 figures. Version 2 is closer to what was published. In particular, a typo in Eq. (8) and in Wg([2^2]) at ref 11 were fixed. Other very minor corrections were done as well

Published
2011

25. Weyl law for fat fractals

Author

Maria Elena Spina, Ignacio García-Mata, and Marcos Saraceno

Subjects
Statistics and Probability, Quantum Physics, FOS: Physical sciences, General Physics and Astronomy, Semiclassical physics, Exterior dimension, Statistical and Nonlinear Physics, Nonlinear Sciences - Chaotic Dynamics, Measure (mathematics), Piecewise linear function, Discontinuity (linguistics), Fractal, Weyl law, Modeling and Simulation, Exponent, Chaotic Dynamics (nlin.CD), Quantum Physics (quant-ph), Mathematical Physics, Mathematical physics, Mathematics
Abstract

It has been conjectured that for a class of piecewise linear maps the closure of the set of images of the discontinuity has the structure of a fat fractal, that is, a fractal with positive measure. An example of such maps is the sawtooth map in the elliptic regime. In this work we analyze this problem quantum mechanically in the semiclassical regime. We find that the fraction of states localized on the unstable set satisfies a modified fractal Weyl law, where the exponent is given by the exterior dimension of the fat fractal., 8 pages, 4 figures, IOP format

Published
2010

26. Irreversibility in quantum maps with decoherence

Author

Diego Ariel Wisniacki, Bernardo Casabone, and Ignacio García-Mata

Subjects
Physics, Quantum Physics, Quantum decoherence, General Mathematics, General Engineering, General Physics and Astronomy, FOS: Physical sciences, Lyapunov exponent, Type (model theory), Nonlinear Sciences - Chaotic Dynamics, Measure (mathematics), Term (time), Coupling (physics), symbols.namesake, symbols, Statistical physics, Sensitivity (control systems), Chaotic Dynamics (nlin.CD), Quantum Physics (quant-ph), Quantum
Abstract

The Bolztmann echo (BE) is a measure of irreversibility and sensitivity to perturbations for non-isolated systems. Recently, different regimes of this quantity were described for chaotic systems. There is a perturbative regime where the BE decays with a rate given by the sum of a term depending on the accuracy with which the system is time-reversed and a term depending on the coupling between the system and the environment. In addition, a parameter independent regime, characterised by the classical Lyapunov exponent, is expected. In this paper we study the behaviour of the BE in hyperbolic maps that are in contact with different environments. We analyse the emergence of the different regimes and show that the behaviour of the decay rate of the BE is strongly dependent on the type of environment., 13 pages, 3 figures.

Published
2010

27. Multifractal wave functions of simple quantum maps

Author

Olivier Giraud, John Martin, Bertrand Georgeot, Ignacio García-Mata, Institut de Physique Nucléaire, Université de Liège, Departamento de Fisica Teorica, GIyAm Comission Nacional de Energia Atomica (TANDAR), Argentina, Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), Centre National de la Recherche Scientifique (CNRS)-Université Paris-Sud - Paris 11 (UP11), Information et Chaos Quantiques (LPT), 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, 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), and Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)

Subjects
Sigma model, Condensed Matter - Mesoscale and Nanoscale Physics, FOS: Physical sciences, Multifractal system, Eigenfunction, Nonlinear Sciences - Chaotic Dynamics, 01 natural sciences, Condensed Matter::Disordered Systems and Neural Networks, Quantum chaos, 010305 fluids & plasmas, Nonlinear system, Fractal, Wavelet, [PHYS.COND.CM-GEN]Physics [physics]/Condensed Matter [cond-mat]/Other [cond-mat.other], 0103 physical sciences, [NLIN.NLIN-CD]Nonlinear Sciences [physics]/Chaotic Dynamics [nlin.CD], Mesoscale and Nanoscale Physics (cond-mat.mes-hall), Statistical physics, Chaotic Dynamics (nlin.CD), 010306 general physics, Wave function, Mathematics
Abstract

We study numerically multifractal properties of two models of one-dimensional quantum maps, a map with pseudointegrable dynamics and intermediate spectral statistics, and a map with an Anderson-like transition recently implemented with cold atoms. Using extensive numerical simulations, we compute the multifractal exponents of quantum wave functions and study their properties, with the help of two different numerical methods used for classical multifractal systems (box-counting method and wavelet method). We compare the results of the two methods over a wide range of values. We show that the wave functions of the Anderson map display a multifractal behavior similar to eigenfunctions of the three-dimensional Anderson transition but of a weaker type. Wave functions of the intermediate map share some common properties with eigenfunctions at the Anderson transition (two sets of multifractal exponents, with similar asymptotic behavior), but other properties are markedly different (large linear regime for multifractal exponents even for strong multifractality, different distributions of moments of wave functions, absence of symmetry of the exponents). Our results thus indicate that the intermediate map presents original properties, different from certain characteristics of the Anderson transition derived from the nonlinear sigma model. We also discuss the importance of finite-size effects., Comment: 15 pages, 21 figures

Published
2010
Full Text
View/download PDF

28. Nonlinear delocalization on disordered Stark ladder

Author

Dima L. Shepelyansky, Ignacio García-Mata, Information et Chaos Quantiques (LPT), 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), ANR NANOTERRA, ANR-08-NANO-0018,NANOTERRA,Nanodetecteurs de radiation microondes et terahertz bases sur l' effet ratchet(2008), 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
Wave packet, Complex system, FOS: Physical sciences, Quantum entanglement, 01 natural sciences, Condensed Matter::Disordered Systems and Neural Networks, 010305 fluids & plasmas, Schrödinger equation, symbols.namesake, Delocalized electron, 0103 physical sciences, 010306 general physics, Physics, Quantum Physics, Condensed matter physics, Disordered Systems and Neural Networks (cond-mat.dis-nn), Condensed Matter - Disordered Systems and Neural Networks, Nonlinear Sciences - Chaotic Dynamics, Condensed Matter Physics, Electronic, Optical and Magnetic Materials, Nonlinear system, Stark effect, [PHYS.COND.CM-GEN]Physics [physics]/Condensed Matter [cond-mat]/Other [cond-mat.other], symbols, Exponent, Chaotic Dynamics (nlin.CD), Quantum Physics (quant-ph)
Abstract

We study effects of weak nonlineary on localization of waves in disordered Stark ladder corresponding to propagation in presence of disorder and a static field. Our numerical results show that nonlinearity leads to delocalization with subdiffusive spreading along the ladder. The exponent of spreading remains close to its value in absence of the static field., Comment: Research found at http://www.quantware.ups-tlse.fr/

Published
2009

29. Delocalization induced by nonlinearity in systems with disorder

Author

Ignacio García-Mata, Dima L. Shepelyansky, Information et Chaos Quantiques (LPT), 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, 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), and Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)

Subjects
Quantum Physics, Anderson localization, nonlinearity, FOS: Physical sciences, Perturbation (astronomy), Disordered Systems and Neural Networks (cond-mat.dis-nn), Condensed Matter - Disordered Systems and Neural Networks, Nonlinear Sciences - Chaotic Dynamics, Critical value, 01 natural sciences, 010305 fluids & plasmas, Nonlinear system, Delocalized electron, [PHYS.COND.CM-GEN]Physics [physics]/Condensed Matter [cond-mat]/Other [cond-mat.other], Quantum mechanics, Lattice (order), 0103 physical sciences, Chaotic Dynamics (nlin.CD), Algebraic number, Quantum Physics (quant-ph), 010306 general physics, Mathematics, Dimensionless quantity
Abstract

We study numerically the effects of nonlinearity on the Anderson localization in lattices with disorder in one and two dimensions. The obtained results show that at moderate strength of nonlinearity an unlimited spreading over the lattice in time takes place with an algebraic growth of number of populated sites $\Delta n \propto t^{\nu}$. The numerical values of $\nu$ are found to be approximately $0.15 - 0.2$ and 0.25 for the dimension $d=1$ and 2 respectively being in a satisfactory agreement with the theoretical value $d/(3d+2)$. The localization is preserved below a certain critical value of nonlinearity. We also discuss the properties of the fidelity decay induced by a perturbation of nonlinear field., Comment: 8 pages, 13 figures. New data and references added. Research at http://www.quantware.ups-tlse.fr/

Published
2009

30. Quantum computation of multifractal exponents through the quantum wavelet transform

Author

Olivier Giraud, Bertrand Georgeot, Ignacio García-Mata, Information et Chaos Quantiques (LPT), 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, FOS: Physical sciences, Quantum simulator, Multifractal system, 01 natural sciences, Condensed Matter::Disordered Systems and Neural Networks, Atomic and Molecular Physics, and Optics, Quantum chaos, 010305 fluids & plasmas, [PHYS.QPHY]Physics [physics]/Quantum Physics [quant-ph], Quantum state, Quantum mechanics, 0103 physical sciences, Quantum phase estimation algorithm, Quantum algorithm, Statistical physics, Quantum information, Quantum Physics (quant-ph), 010306 general physics, Quantum computer
Abstract

We study the use of the quantum wavelet transform to extract efficiently information about the multifractal exponents for multifractal quantum states. We show that, combined with quantum simulation algorithms, it enables to build quantum algorithms for multifractal exponents with a polynomial gain compared to classical simulations. Numerical results indicate that a rough estimate of fractality could be obtained exponentially fast. Our findings are relevant e.g. for quantum simulations of multifractal quantum maps and of the Anderson model at the metal-insulator transition., 9 pages, 9 figures

Published
2008

31. Shor's factorization algorithm with a single control qubit and imperfections

Author

Ignacio García-Mata, Dima L. Shepelyansky, Klaus M. Frahm, Information et Chaos Quantiques (LPT), 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, Quantum Physics, Computation, Shor's algorithm, Many-body theory, FOS: Physical sciences, Disordered Systems and Neural Networks (cond-mat.dis-nn), Condensed Matter - Disordered Systems and Neural Networks, 01 natural sciences, Atomic and Molecular Physics, and Optics, Quantum chaos, 010305 fluids & plasmas, Computer Science::Emerging Technologies, Factorization, [PHYS.QPHY]Physics [physics]/Quantum Physics [quant-ph], Qubit, 0103 physical sciences, Quantum Physics (quant-ph), 010306 general physics, Algorithm, Scaling, Quantum computer
Abstract

We formulate and numerically simulate the single control qubit Shor algorithm for the case of static imperfections induced by residual couplings between qubits. This allows us to study the accuracy of Shor's algorithm with respect to these imperfections using numerical simulations of realistic quantum computations with up to $n_q=18$ computational qubits allowing to factor numbers up to N=205193. We confirm that the algorithm remains operational up to a critical coupling strength $\epsilon_c$ which drops only polynomially with $\log_2 N$. The obtained numerical dependence of $\epsilon_c$ on $\log_2 N$ is in a good agreement with the analytical estimates that allows to obtain the scaling for functionality of Shor's algorithm on realistic quantum computers with a large number of qubits., Comment: 9 pages 5 figures, and 1 table. Research at http://www.quantware.ups-tlse.fr/

Published
2008

32. Erratum: Effects of imperfections for Shor’s factorization algorithm [Phys. Rev. A75, 052311 (2007)]

Author

Ignacio García-Mata, Dima L. Shepelyansky, and Klaus M. Frahm

Subjects
Physics, Reduction (recursion theory), Factorization, Quantum error correction, Quantum mechanics, Inverse, Quantum algorithm, Statistical physics, Function (mathematics), Algebraic number, Atomic and Molecular Physics, and Optics, Quantum computer
Abstract

There is an error in the numerical implementation of the static imperfection model Eq. 21 in the paper , which resulted in an effective reduction of the disorder strength by approximately a factor of 2 for the cases of generic and correlated imperfection models. However, there was no error for the correlated imperfection model with all qubits in the control and computational register coupled by interactions. After correction of the error the dependence of the inverse participation ratio IPR on see Fig. 1 a remains qualitatively the same as in Fig. 6 of the paper. Nevertheless, the values of c fluctuate strongly depending on the arithmetic properties of x, r, and N. These fluctuations remain quite strong even after increasing the number of data points see Table II in 1 and Fig. 1 b as compared to Table I and Fig. 10 of the paper . The algebraic fit c=B / log2 N gives ln B=0.068±0.105, =1.420±0.054 for the generic imperfection model, ln B=0.70±0.19, =1.897±0.097 for the correlated imperfection model, and ln B=−1.22±0.13, =1.523±0.068 for the correlated imperfection model with all qubits coupled. We attribute the deviations of the exponents from the theoretical values to finite size effects in number of qubits and the significant arithmetic fluctuations of c as a function of r, x, and N. In addition after publication we realized there were two typos in Eqs. 22 and 26 which should read

Published
2007

33. Effects of imperfections for Shor's factorization algorithm

Author

Klaus M. Frahm, Ignacio García-Mata, Dima L. Shepelyansky, Information et Chaos Quantiques (LPT), 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, EC IST-FET project EUROSQIP, 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 (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
Physics, Quantum Physics, Computation, Shor's algorithm, Many-body theory, FOS: Physical sciences, 01 natural sciences, Atomic and Molecular Physics, and Optics, Quantum chaos, 010305 fluids & plasmas, Computer Science::Emerging Technologies, Factorization, [PHYS.QPHY]Physics [physics]/Quantum Physics [quant-ph], Qubit, 0103 physical sciences, Quantum Physics (quant-ph), 010306 general physics, Scaling, Algorithm, Quantum computer
Abstract

We study effects of imperfections induced by residual couplings between qubits on the accuracy of Shor's algorithm using numerical simulations of realistic quantum computations with up to 30 qubits. The factoring of numbers up to N=943 show that the width of peaks, which frequencies allow to determine the factors, grow exponentially with the number of qubits. However, the algorithm remains operational up to a critical coupling strength $\epsilon_c$ which drops only polynomially with $\log_2 N$. The numerical dependence of $\epsilon_c$ on $\log_2 N$ is explained by analytical estimates that allows to obtain the scaling for functionality of Shor's algorithm on realistic quantum computers with a large number of qubits., Comment: 10 pages, 10 figures, 1 table. Added references and new data. Erratum added as appendix. 1 Figure and 1 Table added. Research is available at http://www.quantware.ups-tlse.fr/

Published
2007

34. Quantum phase estimation algorithm in presence of static imperfections

Author

Dima L. Shepelyansky, Ignacio García-Mata, Information et Chaos Quantiques (LPT), 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
Physics, Quantum Physics, Condensed Matter - Superconductivity, FOS: Physical sciences, Residual, 01 natural sciences, Atomic and Molecular Physics, and Optics, 010305 fluids & plasmas, Superconductivity (cond-mat.supr-con), Quantum gate, Computer Science::Emerging Technologies, [PHYS.QPHY]Physics [physics]/Quantum Physics [quant-ph], Qubit, Random noise, 0103 physical sciences, Quantum phase estimation algorithm, Statistical physics, Hardware_ARITHMETICANDLOGICSTRUCTURES, 010306 general physics, Quantum Physics (quant-ph)
Abstract

We study numerically the effects of static imperfections and residual couplings between qubits for the quantum phase estimation algorithm with two qubits. We show that the success probability of the algorithm is affected significantly more by static imperfections than by random noise errors in quantum gates. An improvement of the algorithm accuracy can be reached by application of the Pauli-random-error-correction method (PAREC)., Comment: 5 pages, 5 figures. Research avilable at http://www.quantware.ups-tlse.fr/

Published
2007
Full Text
View/download PDF

35. Entanglement screening by nonlinear resonances

Author

Ignacio García-Mata, André R. R. Carvalho, Florian Mintert, Andreas Buchleitner, Information et Chaos Quantiques (LPT), 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, Quantum decoherence, General Physics and Astronomy, Semiclassical physics, FOS: Physical sciences, Quantum entanglement, Squashed entanglement, Multipartite entanglement, Multipartite, [PHYS.QPHY]Physics [physics]/Quantum Physics [quant-ph], Quantum state, Quantum mechanics, [NLIN.NLIN-CD]Nonlinear Sciences [physics]/Chaotic Dynamics [nlin.CD], W state, Quantum Physics (quant-ph)
Abstract

We show that nonlinear resonances in a classically mixed phase space allow to define generic, strongly entangled multi-partite quantum states. The robustness of their multipartite entanglement increases with the particle number, i.e. in the semiclassical limit, for those classes of diffusive noise which assist the quantum-classical transition., Comment: 4 pages, 3 figures. PRL, in press

Published
2006

36. Spectral Approach to Chaos and Quantum-Classical Correspondence in Quantum Mapas

Author

Marcos Saraceno and Ignacio García-Mata

Subjects
Physics, Spectral approach, Quantum Physics, Superoperator, Spectrum (functional analysis), FOS: Physical sciences, Propagator, Statistical and Nonlinear Physics, Condensed Matter Physics, Nonlinear Sciences - Chaotic Dynamics, Noise (electronics), CHAOS (operating system), Nonlinear Sciences::Chaotic Dynamics, Quantum mechanics, Chaotic Dynamics (nlin.CD), Quantum Physics (quant-ph), Quantum, Eigenvalues and eigenvectors
Abstract

Correspondence in quantum chaotic systems is lost in short time scales. Introducing some noise we study the spectrum of the resulting coarse grained propagaor of density matrices. Some differen methods to compute the spectrum are reviewed. Moreover, the relationship between the eigenvalues of the coarse-grained superoperator and the classical Ruelle-Pollicott resonances is remarked. As a concequence, classical decay rates in quantum time dependent quantities appear., Brief Review to appear in the April '05 Issue of Mod. Phys. Lett. B (World Scientific)

Published
2005

37. Phase space contraction and quantum operations

Author

Maria Elena Spina, Marcos Saraceno, Gabriel G. Carlo, and Ignacio García-Mata

Subjects
Physics, Quantum Physics, FOS: Physical sciences, Quantum capacity, Nonlinear Sciences - Chaotic Dynamics, Atomic and Molecular Physics, and Optics, Quantum technology, Open quantum system, Classical mechanics, Quantum process, Quantum operation, Quantum algorithm, Quantum information, Chaotic Dynamics (nlin.CD), Amplitude damping channel, Quantum Physics (quant-ph)
Abstract

We give a criterion to differentiate between dissipative and diffusive quantum operations. It is based on the classical idea that dissipative processes contract volumes in phase space. We define a quantity that can be regarded as ``quantum phase space contraction rate'' and which is related to a fundamental property of quantum channels: non-unitality. We relate it to other properties of the channel and also show a simple example of dissipative noise composed with a chaotic map. The emergence of attaractor-like structures is displayed., Comment: 8 pages, 6 figures. Changes added according to refferee sugestions. (To appear in PRA)

Published
2005
Full Text
View/download PDF

38. Noise models for superoperators in the chord representation

Author

Ignacio García-Mata, Mario Leandro Aolita, and Marcos Saraceno

Subjects
Physics, Quantum Physics, Chord (geometry), Quantum decoherence, Superoperator, Quantum noise, FOS: Physical sciences, Nonlinear Sciences - Chaotic Dynamics, Atomic and Molecular Physics, and Optics, Open quantum system, Quantum error correction, Phase space, Statistical physics, Chaotic Dynamics (nlin.CD), Quantum Physics (quant-ph), Quantum dissipation
Abstract

We study many-qubit generalizations of quantum noise channels that can be written as an incoherent sum of translations in phase space. Physical description in terms of the spectral properties of the superoperator and the action in phase space are provided. A very natural description of decoherence leading to a preferred basis is achieved with diffusion along a phase space line. The numerical advantages of using the chord representation are illustrated in the case of coarse-graining noise., 8 pages, 5 .ps figures (RevTeX4). Submitted to Phys. Rev. A. minor changes made, according to referee suggestions

Published
2004

39. Spectral properties and classical decays in quantum open systems

Author

Ignacio García-Mata and Marcos Saraceno

Subjects
Physics, Quantum Physics, Quantum dynamics, FOS: Physical sciences, Nonlinear Sciences - Chaotic Dynamics, Quantum chaos, Nonlinear Sciences::Chaotic Dynamics, Open quantum system, Theoretical physics, Classical mechanics, Quantum state, Quantum process, Quantum operation, Chaotic Dynamics (nlin.CD), Quantum Physics (quant-ph), Quantum dissipation, Quantum statistical mechanics
Abstract

We study the relationship between the spectral properties of diffusive open quantum maps and the classical spectrum of Ruelle-Pollicott resonances. The leading resonances determine the asymptotic time regime for several quantities of interest - the linear entropy, the Loschmidt echo and the correlations of the initial state. A numerical method that allow an efficient calculation of the leading spectrum is developed using a truncated basis adapted to the dynamics., 14 pages, 8 figures. submitted to PRE. Typos corrected. Refferences added. Fig 5 corrected. Some changes following refferees' sugestions made

Published
2003

40. Classical decays in decoherent quantum maps

Author

Marcos Saraceno, María Elena Spina, and Ignacio García-Mata

Subjects
Physics, Quantum discord, Quantum Physics, Mathematics::Dynamical Systems, Quantum dynamics, General Physics and Astronomy, FOS: Physical sciences, Quantum channel, Nonlinear Sciences - Chaotic Dynamics, Quantum chaos, Classical capacity, Nonlinear Sciences::Chaotic Dynamics, Open quantum system, Quantum mechanics, Quantum process, Statistical physics, Quantum information, Chaotic Dynamics (nlin.CD), Quantum Physics (quant-ph)
Abstract

We study the asymptotic long-time behavior of open quantum maps and relate the decays to the eigenvalues of a coarse-grained superoperator. In specific ranges of coarse graining, and for chaotic maps, these decay rates are given by the Ruelle-Pollicott resonances of the classical map., Comment: 4 pages, 4 figures. Refference added. Submitted to PRL

Published
2003
Full Text
View/download PDF

41. Random walk with an exponentially varying step

Author

Ignacio García-Mata, Pedro J. Catuogno, A. de la Torre, Hector Omar Martin, and Alberto Maltz

Subjects
Distribution (mathematics), Fractal, Position (vector), Path (graph theory), Mathematical analysis, Probability density function, Interval (mathematics), Diffusion (business), Random walk, Mathematics
Abstract

A random walk with exponentially varying step, modeling damped or amplified diffusion, is studied. Each step is equal to the previous one multiplied by a step factor s (0sinfinity). There is a symmetry under the transformation s--1/s relating different processes. For s1/2 and s2, the process is retrodictive (i.e., every final position can be reached by a unique path) and the set of all possible final points after infinite steps is fractal. For step factors in the interval [1/2,2], some cases result in smooth density distributions, other cases present overlapping self-similarity and there are values of the step factor for which the distribution is singular without a density function.

Published
2000

42. The photon-box Bohr-Einstein debate demythologized. Reply to Comment *

Author

Ignacio García-Mata, A Daleo, and A. de la Torre

Subjects
Physics, symbols.namesake, Photon, Argument, symbols, medicine, General Physics and Astronomy, Criticism, Einstein, medicine.symptom, Confusion, Epistemology, Bohr model
Abstract

The arguments presented in the criticism of our work suffer from the same mistakes that we have denounced. That is, the confusion of quantum indeterminacies with experimental uncertainties. We mention another example of how this type of argument can lead to wrong results and we show other weaknesses of the debate.

Published
2002

43. Semiclassical approach to fidelity amplitude

Author

Raúl O. Vallejos, Ignacio García-Mata, and Diego Ariel Wisniacki

Subjects
Lyapunov function, Physics, Quantum Physics, media_common.quotation_subject, Chaotic, FOS: Physical sciences, General Physics and Astronomy, Perturbation (astronomy), Semiclassical physics, Fidelity, Random perturbation, Nonlinear Sciences - Chaotic Dynamics, Nonlinear Sciences::Chaotic Dynamics, symbols.namesake, Amplitude, symbols, Statistical physics, Chaotic Dynamics (nlin.CD), Quantum Physics (quant-ph), Quantum, media_common
Abstract

The fidelity amplitude is a quantity of paramount importance in echo type experiments. We use semiclassical theory to study the average fidelity amplitude for quantum chaotic systems under external perturbation. We explain analytically two extreme cases: the random dynamics limit --attained approximately by strongly chaotic systems-- and the random perturbation limit, which shows a Lyapunov decay. Numerical simulations help us bridge the gap between both extreme cases., 10 pages, 9 figures. Version closest to published version

Published
2011

44. Loschmidt echo in quantum maps: the elusive nature of the Lyapunov regime

Author

Diego Ariel Wisniacki and Ignacio García-Mata

Subjects
Statistics and Probability, Lyapunov function, Physics, Quantum Physics, FOS: Physical sciences, General Physics and Astronomy, Semiclassical physics, Statistical and Nonlinear Physics, Lyapunov exponent, Nonlinear Sciences - Chaotic Dynamics, Quantum evolution, Nonlinear Sciences::Chaotic Dynamics, symbols.namesake, Amplitude, Modeling and Simulation, symbols, Statistical physics, Chaotic Dynamics (nlin.CD), Exponential decay, Quantum Physics (quant-ph), Hamiltonian (quantum mechanics), Quantum, Mathematical Physics
Abstract

The Loschmidt echo is a measure of the stability and reversibility of quantum evolution under perturbations of the Hamiltonian. One of the expected and most relevant characteristics of this quantity for chaotic systems is an exponential decay with a perturbation independent decay rate given by the classical Lyapunov exponent. However, a non-uniform decay -- instead of the Lyapunov regime -- has been reported in several systems. In this work we find an analytical semiclassical expression for the averaged fidelity amplitude that can be related directly to the anomalous -- unexpected-- behaviour of the LE., 16 pages, 6 figures. IOP format. Substantial changes with respect to v1. Accepted in J. Phys. A: Math. Theo

Published
2011

45. Discrepancies between decoherence and the Loschmidt echo

Author

Ignacio García-Mata, Diego Ariel Wisniacki, and Bernardo Casabone

Subjects
Physics, Quantum Physics, Quantum decoherence, Hilbert space, FOS: Physical sciences, General Physics and Astronomy, Nonlinear Sciences - Chaotic Dynamics, Instability, Nonlinear Sciences::Chaotic Dynamics, symbols.namesake, Chaotic systems, symbols, Quantum system, Statistical physics, Chaotic Dynamics (nlin.CD), Quantum Physics (quant-ph), Coherence (physics)
Abstract

The Loschmidt echo and the purity are two quantities that can provide invaluable information about the evolution of a quantum system. While the Loschmidt echo characterizes instability and sensitivity to perturbations, purity measures the loss of coherence produced by an environment coupled to the system. For classically chaotic systems both quantities display a number of -- supposedly universal -- regimes that can lead on to think of them as equivalent quantities. We study the decay of the Loschmidt echo and the purity for systems with finite dimensional Hilbert space and present numerical evidence of some fundamental differences between them., 6 pages, 3 figures. Changed title. Added 1 figure. Published version.

Published
2010

46. Irreversibility in quantum maps with decoherence.

Author

Ignacio García-Mata

Subjects
*QUANTUM maps, *LYAPUNOV exponents, *MATHEMATICAL mappings, *QUANTUM chaos, *PERTURBATION theory
Abstract

The Boltzmann echo (BE) is a measure of irreversibility and sensitivity to perturbations for non-isolated systems. Recently, different regimes of this quantity were described for chaotic systems. There is a perturbative regime where the BE decays with a rate given by the sum of a term depending on the accuracy with which the system is time reversed and a term depending on the coupling between the system and the environment. In addition, a parameter-independent regime, characterized by the classical Lyapunov exponent, is expected. In this paper, we study the behaviour of the BE in hyperbolic maps that are in contact with different environments. We analyse the emergence of the different regimes and show that the behaviour of the decay rate of the BE is strongly dependent on the type of environment. [ABSTRACT FROM AUTHOR]

Published
2011
Full Text
View/download PDF

Catalog

Books, media, physical & digital resources
See catalog results