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International audience; The Efimov window, or universal window, is a particular energy region in which few-body systems are loosely bound. Many characteristics of those systems are universal; their properties are largely independent of the particular interaction that produces the binding. This suggests the use of simple potential models characterized by few parameters to describe dynamical properties. Essentially, the potential parameters are set in order to reproduce a small number of data, and then the potential strength can be varied to explore the window. Among others, the Gaussian potential has been used to characterize the universal window. From calculations of the ground state and of the first excited state of three identical bosons using a Gaussian potential along the window, we determine what is called the gaussian-level function. This function is independent of the particular Gaussian potential used in this procedure. Moreover, it contains finite-range corrections which are of particular importance when theoretical predictions are compared to experimental data.

Physical systems characterized by a shallow two-body bound or virtual state are governed at large distances by a continuous-scale invariance, which is broken to a discrete one when three or more particles come into play. This symmetry induces a universal behavior for different systems, independent of the details of the underlying interaction, rooted in the smallness of the ratio $\ell/a_B \ll 1$, where the length $a_B$ is associated to the binding energy of the two-body system $E_2=\hbar^2/m a_B^2$ and $\ell$ is the natural length given by the interaction range. Efimov physics refers to this universal behavior, which is often hidden by the on-set of system-specific non-universal effects. In this work we identify universal properties by providing an explicit link of physical systems to their unitary limit, in which $a_B\rightarrow\infty$, and show that nuclear systems belong to this class of universality., 27 pages, 8 figures

International audience; The Hohenberg-Kohn theorem and the Kohn-Sham equations, which are at the basis of the density-functional theory, are reformulated in terms of a particular many-body density, which is translational and Galilean invariant and therefore is relevant for self-bound systems. In a similar way that there is a unique relation between the one-body density and the external potential that gives rise to it, we demonstrate that there is a unique relation between that particular many-body density and a definite many-body potential. The energy is then a functional of this density, and its minimization leads to the ground-state energy of the system. As a proof of principle, the analogous of the Kohn-Sham equation is solved in the specific case of He4 atomic clusters, to put in evidence the advantages of this formulation in terms of physical insights.

Neural-network quantum states have shown great potential for the study of many-body quantum systems. In statistical machine learning, transfer learning designates protocols reusing features of a machine learning model trained for a problem to solve a possibly related but different problem. We propose to evaluate the potential of transfer learning to improve the scalability of neural-network quantum states. We devise and present physics-inspired transfer learning protocols, reusing the features of neural-network quantum states learned for the computation of the ground state of a small system for systems of larger sizes. We implement different protocols for restricted Boltzmann machines on general-purpose graphics processing units. This implementation alone yields a speedup over existing implementations on multi-core and distributed central processing units in comparable settings. We empirically and comparatively evaluate the efficiency (time) and effectiveness (accuracy) of different transfer learning protocols as we scale the system size in different models and different quantum phases. Namely, we consider both the transverse field Ising and Heisenberg XXZ models in one dimension, and also in two dimensions for the latter, with system sizes up to 128 and 8 x 8 spins. We empirically demonstrate that some of the transfer learning protocols that we have devised can be far more effective and efficient than starting from neural-network quantum states with randomly initialized parameters., 13 pages, 11 figures

Universal behavior in few-boson systems close to the unitary limit, where two bosons become unbound, has been intensively investigated in recent years both experimentally and theoretically. In this particular region, called the unitary window, details of the interparticle interactions are not important and observables, such as binding energies, can be characterized by a few parameters. With an increasing number of particles, the short-range repulsion, present in all atomic, molecular, and nuclear interactions, gradually induces deviations from the universal behavior. In the present paper, we discuss a simple way of incorporating nonuniversal behavior through one specific parameter which controls the smooth transition of the system from a universal to nonuniversal regime. Using a system of $N$ helium atoms as an example, we calculate their ground-state energies as trajectories within the unitary window and also show that the control parameters can be used to determine the energy per particle in homogeneous systems when $N\ensuremath{\rightarrow}\ensuremath{\infty}$.

Efimov states are a sequence of shallow three-body bound states that arise when the two-body scattering length is much larger than the range of the interaction. The binding energies of these states are described as a function of the scattering length and one three-body parameter by a transcendental equation involving a universal function of one angular variable. We provide an accurate and convenient parametrization of this function. Moreover, we discuss the effective treatment of range corrections in the universal equation and compare with a strictly perturbative scheme., 13 pages, 5 figures

International audience; The large values of the singlet and triplet scattering lengths locate the two-nucleon system close to the unitary limit, the limit in which these two values diverge. As a consequence, the system shows a continuous scale invariance, which strongly constrains the values of the observables, a well-known fact already noticed a long time ago. For example, the triton binding energy is correlated with other observables such as the doublet nucleon-deuteron scattering length or the α-particle binding energy. Moreover, the low-energy dynamics of these systems is universal; it does not depend on the details of the nuclear interaction. Instead, it depends on a few control parameters such as the (large) values of the scattering lengths and the triton binding energy. Using a potential model in order to vary the values of the scattering lengths, we study the spectrum of A=2,3,4,6 nuclei in the region between the unitary limit and the point where the scattering lengths get their physical values. In particular, we analyze how the binding energies emerge from the unitary limit forming the observed levels.

When the binding energy of a two-body system goes to zero the two-body system shows a continuous scaling invariance governed by the large value of the scattering length. In the case of three identical bosons, the three-body system in the same limit shows the Efimov effect and the scale invariance is broken to a discrete scale invariance. As the number of bosons increases correlations appear between the binding energy of the few- and many-body systems. We discuss some of them as the relation between the saturation properties of the infinite system and the low-energy properties of the few-boson system., 6 pages, 3 figures. Contribution to the proceedings of the XXII International Conference on Few-Body Problems in Physics (FB22) (Caen, France, July 2018)

International audience; The understanding of nuclear systems as composed of interacting nucleons has been considerably sharpened by the effective field theory (EFT) framework. The latter provides a link between the nuclear interaction and the underlying quantum chromodynamics, as the relevant degrees of freedom result, at least ideally, from a decimation process starting from fundamental quarks and gluons. Owing to chiral symmetry and the Goldstone bosons’ characters of the interchanged pions among nucleons, the properties of heavier nuclei can in principle be traced back to a restricted set of low-energy constants (LECs) to be determined in lighter systems in the framework of a systematic low-energy expansion. At smaller energy scales, in pionless EFT, the interactions simplify becoming of contact type. The low-energy expansion is organized differently, relying on the emergence of universal properties, characteristic of systems with large two-body scattering lengths. We will examine the two above schemes and discuss their relation, with the aim of devising viable power counting schemes for applications in nuclear physics.

In chiral effective field theory the leading order (LO) nucleon-nucleon potential includes two contact terms, in the two spin channels $S=0,1$, and the one-pion-exchange potential. When the pion degrees of freedom are integrated out, as in the pionless effective field theory, the LO potential includes two contact terms only. In the three-nucleon system, the pionless theory includes a three-nucleon contact term interaction at LO whereas the chiral effective theory does not. Accordingly arbitrary differences could be observed in the LO description of three- and four-nucleon binding energies. We analyze the two theories at LO and conclude that a three-nucleon contact term is necessary at this order in both theories. In turn this implies that subleading three-nucleon contact terms should be promoted to lower orders. Furthermore this analysis shows that one single low energy constant might be sufficient to explain the large values of the singlet and triplet scattering lengths., 5 pages, 3 figures

The universal behavior of a three-boson system close to the unitary limit is encoded in a simple dependence of many observables in terms of few parameters. For example the product of the three-body parameter $\kappa_*$ and the two-body scattering length $a$, $\kappa_* a$ depends on the angle $\xi$ defined by $E_3/E_2=\tan^2\xi$. A similar dependence is observed in the ratio $a_{AD}/a$ with $a_{AD}$ the boson-dimer scattering length. We use a two-parameter potential to determine this simple behavior and, as an application, to compute $a_{AD}$ for the case of three $^4$He atoms., Comment: presented at the 23rd European Conference on Few-Body Problems in Physics

Using potential models we analyze range corrections to the universal law dictated by the Efimov theory of three bosons. In the case of finite-range interactions we have observed that, at first order, it is necessary to supplement the theory with one finite-range parameter, $\Gamma_n^3$, for each specific $n$-level [Kievsky and Gattobigio, Phys. Rev. A {\bf 87}, 052719 (2013)]. The value of $\Gamma_n^3$ depends on the way the potentials is changed to tune the scattering length toward the unitary limit. In this work we analyze a particular path in which the length $r_B=a-a_B$, measuring the difference between the two-body scattering length $a$ and the energy scattering length $a_B$, results almost constant. Analyzing systems with very different scales, as atomic or nuclear systems, we observe that the finite-range parameter remains almost constant along the path with a numerical value of $\Gamma_0^3\approx 0.87$ for the ground state level. This observation suggests the possibility of constructing a single universal function that incorporate finite-range effects for this class of paths. The result is used to estimate the three-body parameter $\kappa_*$ in the case of real atomic systems brought to the unitary limit thought a broad Feshbach resonances. Furthermore, we show that the finite-range parameter can be put in relation with the two-body contact $C_2$ at the unitary limit., Comment: accepted Physical Review A

It is well-known that three-boson systems show the Efimov effect when the two-body scattering length $a$ is large with respect to the range of the two-body interaction. This effect is a manifestation of a discrete scaling invariance (DSI). In this work we study DSI in the $N$-body system by analysing the spectrum of $N$ identical bosons obtained with a pairwise gaussian interaction close to the unitary limit. We consider different universal ratios such as $E_N^0/E_3^0$ and $E_N^1/E_N^0$, with $E_N^i$ being the energy of the ground ($i=0$) and first-excited ($i=1$) state of the system, for $N\le16$. We discuss the extension of the Efimov radial law, derived by Efimov for $N=3$, to general $N$., 4 pages, 3 figures, presented at the 22nd European Conference on Few-Body Problems in Physics, Cracow (Poland)

In this work we investigate small clusters of bosons using the hyperspherical harmonic basis. We consider systems with $A=2,3,4,5,6$ particles interacting through a soft interparticle potential. In order to make contact with a real system, we use an attractive Gaussian potential that reproduces the values of the dimer binding energy and the atom-atom scattering length obtained with one of the most widely used ${}^{4}$He-${}^{4}$He interactions, the LM2M2 potential of Aziz and Slaman. The intensity of the potential is varied in order to explore the clusters' spectra in different regions with large positive and large negative values of the two-body scattering length. In addition, we include a repulsive three-body force to reproduce the trimer binding energy. With this model, consisting in the sum of a two- and three-body potential, we have calculated the spectrum of the four-, five-, and six-particle systems. In all the regions explored, we have found that these systems present two states, one deep and one shallow close to the $A\ensuremath{-}1$ threshold. Some universal relations between the energy levels are extracted; in particular, we have estimated the universal ratios between thresholds of the three-, four-, and five-particle continua using the two-body Gaussian potential. They agree with recent measurements and theoretical predictions.

In this work we show results for light nuclear systems and small clusters of helium atoms using the hyperspherical harmonics basis. We use the basis without previous symmetrization or antisymmetrization of the state. After the diagonalization of the Hamiltonian matrix, the eigenvectors have well defined symmetry under particle permutation and the identification of the physical states is possible. We show results for systems composed up to six particles. As an example of a fermionic system, we consider a nucleon system interacting through the Volkov potential, used many times in the literature. For the case of bosons, we consider helium atoms interacting through a potential model which does not present a strong repulsion at short distances. We have used an attractive gaussian potential to reproduce the values of the dimer binding energy, the atom-atom scattering length, and the effective range obtained with one of the most widely used He-He interaction, the LM2M2 potential. In addition, we include a repulsive hypercentral three-body force to reproduce the trimer binding energy., Presented at the Sixth Workshop on the Critical Stability of Quantum Few-Body Systems, Erice, Sicily, October 2011

We present the exact solution for the many-body wavefunction of a one-dimensional mixture of bosons and spin-polarized fermions with equal masses and infinitely strong repulsive interactions under external confinement. Such a model displays a large degeneracy of the ground state. Using a generalized Bose-Fermi mapping we find the solution for the whole set of ground-state wavefunctions of the degenerate manifold and we characterize them according to group-symmetry considerations. We find that the density profile and the momentum distribution depends on the symmetry of the solution. By combining the wavefunctions of the degenerate manifold with suitable symmetry and guided by the strong-coupling form of the Bethe-Ansatz solution for the homogeneous system we propose an analytic expression for the many-body wavefunction of the inhomogeneous system which well describes the ground state at finite, large and equal interactions strengths, as validated by numerical simulations., 7 pages, 5 figures, final revised version

We study the formation of Faraday waves in an elongated Bose-Einstein condensate in the presence of a one-dimensional optical lattice. The waves are parametrically excited by modulating the radial confinement of the condensate close to a transverse breathing mode of the system. For very shallow optical lattices, phonons with a well-defined wave vector propagate along the condensate, as in the absence of the lattice, and we observe the formation of a Faraday pattern. We find that by increasing the potential depth the local sound velocity decreases, and when it equals the condensate local phase velocity, the condensate develops an incoherent superposition of several modes and the parametric excitation of Faraday waves is suppressed.

The hyperspherical harmonic basis is used to describe bound states in an $A$--body system. The approach presented here is based on the representation of the potential energy in terms of hyperspherical harmonic functions. Using this representation, the matrix elements between the basis elements are simple, and the potential energy is presented in a compact form, well suited for numerical implementation. The basis is neither symmetrized nor antisymmetrized, as required in the case of identical particles; however, after the diagonalization of the Hamiltonian matrix, the eigenvectors reflect the symmetries present in it, and the identification of the physical states is possible, as it will be shown in specific cases. We have in mind applications to atomic, molecular, and nuclear few-body systems in which symmetry breaking terms are present in the Hamiltonian; their inclusion is straightforward in the present method. As an example we solve the case of three and four particles interacting through a short-range central interaction and Coulomb potential.

We discuss specific noise phenomena in several ballistic mesoscopic structures and in networks of quantum dots or metallic dots interconnected by tunneling barriers, focusing on the techniques used for the numerical simulation and on the physical interpretation of the results.

A prototype cell for the investigation of QCA (quantum cellular automaton) functionality in silicon-on-insulator technology has been fabricated and characterized, observing interaction between the upper and the lower double dots. A simulation code, validated by comparison with the experimental results, has been used to design a modified layout that should allow demonstration of QCA operation at temperatures above 0.3 K.

We present the peculiar noise behavior of bistable systems of coupled quantum dots during switching between the two stable states. Shot noise of the current through different branches of the system can be suppressed and/or enhanced up to a few times the ``full'' shot-noise level. Results from Monte Carlo simulations and from an analytical model are presented.

We present a proposal for an experiment to demonstrate QCA (Quantum Cellular Automaton) functionality for a cell fabricated with silicon-on-insulator technology. The fundamental feature of a working QCA cell consists in the anticorrelated transition of electrons in the two pairs of dots forming the cell: we show how such a phenomenon can be detected from the appearance of a “locking” effect between the Coulomb Blockade current peaks relative to each pair. The proposed approach allows the detection of QCA action without the need for additional noninvasive charge detectors probing each dot. We have performed detailed numerical simulations on the basis of interdot capacitance values obtained from experimental data and determined the range of parameters within which the effect should be detectable.

The nonlinear Schrodinger equation on the half line with mixed boundary condition is investigated. After a brief introduction to the corresponding classical boundary value problem, the exact second quantized solution of the system is constructed. The construction is based on a new algebraic structure, which is called in what follows boundary algebra and which substitutes, in the presence of boundaries, the familiar Zamolodchikov-Faddeev algebra. The fundamental quantum field theory properties of the solution are established and discussed in detail. The relative scattering operator is derived in the Haag-Ruelle framework, suitably generalized to the case of broken translation invariance in space., Tex file, no figures, 32 pages

We establish the second quantized solution of the nonlinear Schrodinger equation on the half line with a mixed boundary condition. The solution is based on a new algebraic structure, which we call boundary exchange algebra and which substitutes, in the presence of boundaries, the familiar Zamolodchikov-Faddeev algebra., Revtex file, no figures, 8 pages