The degree of chaos in the simplest interacting boson model (IBM-1) is compared with what we call the ``dynamical symmetry content'' of the system. The latter is represented by the information entropy of the eigenfunctions with respect to bases associated with dynamical symmetries of the IBM-1, and expresses thus the localization of actual eigenfunctions in these symmetry bases. The wave-function entropy is shown to be a sensitive tool for monitoring the processes of a single dynamical symmetry breaking or transitions between two and more symmetries. For the IBM-1 Hamiltonians studied here, the known features related to chaos, namely, the dependence of chaotic measures on the Hamiltonian parameters (position in the Casten triangle) and on the angular momentum, turn out to be correlated with the behavior of the wave-function entropy.The degree of chaos in the simplest interacting boson model (IBM-1) is compared with what we call the ``dynamical symmetry content'' of the system. The latter is represented by the information entropy of the eigenfunctions with respect to bases associated with dynamical symmetries of the IBM-1, and expresses thus the localization of actual eigenfunctions in these symmetry bases. The wave-function entropy is shown to be a sensitive tool for monitoring the processes of a single dynamical symmetry breaking or transitions between two and more symmetries. For the IBM-1 Hamiltonians studied here, the known features related to chaos, namely, the dependence of chaotic measures on the Hamiltonian parameters (position in the Casten triangle) and on the angular momentum, turn out to be correlated with the behavior of the wave-function entropy.

arXiv:chao-dyn/9802024Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topicsJul 1, 199843 citations

Random k-Body Ensembles for Chaos and Thermalization in Isolated Systems

V. K. B. Kota, N. D. Chavda

Embedded ensembles or random matrix ensembles generated by k-body interactions acting in many-particle spaces are now well established to be paradigmatic models for many-body chaos and thermalization in isolated finite quantum (fermion or boson) systems. In this article, briefly discussed are (i) various embedded ensembles with Lie algebraic symmetries for fermion and boson systems and their extensions (for Majorana fermions, with point group symmetries etc.); (ii) results generated by these ensembles for various aspects of chaos, thermalization and statistical relaxation, including the role of q-hermite polynomials in k-body ensembles; and (iii) analyses of numerical and experimental data for level fluctuations for trapped boson systems and results for statistical relaxation and decoherence in these systems with close relations to results from embedded ensembles.Embedded ensembles or random matrix ensembles generated by k-body interactions acting in many-particle spaces are now well established to be paradigmatic models for many-body chaos and thermalization in isolated finite quantum (fermion or boson) systems. In this article, briefly discussed are (i) various embedded ensembles with Lie algebraic symmetries for fermion and boson systems and their extensions (for Majorana fermions, with point group symmetries etc.); (ii) results generated by these ensembles for various aspects of chaos, thermalization and statistical relaxation, including the role of q-hermite polynomials in k-body ensembles; and (iii) analyses of numerical and experimental data for level fluctuations for trapped boson systems and results for statistical relaxation and decoherence in these systems with close relations to results from embedded ensembles.

EntropyJul 20, 201811 citations

NEW ASPECTS OF THE INTERACTING BOSON MODEL

E. Nadzhakov, I.N. Mikhailov

Oct 6, 19870 citations

Interacting 1D Chiral Fermions with Pairing: Transition from Integrable to Chaotic

Biao Lian

We study a generic one-dimensonal quantum model of two flavors (pseudospins) chiral complex fermions by exact diagonalization, which can have local interflavor interaction and superconducting pairings (with all irrelevant terms ignored). Analytically, the model has two solvable (integrable) points in the parameter space: it is a free fermion model when the fermion interaction is zero, and is a free boson Luttinger liquid when there is a global U(1) $^{(\uparrow)}\times$ U(1) $^{(\downarrow)}$ symmetry (with nonzero interaction). When the global symmetry of the interacting model is lowered by turning on symmetry breaking parameters, the model undergoes a transition from a quantum integrable model to a fully quantum chaotic model, as we demonstrate by examining the level spacing statistics (LSS) of the many-body energy spectrum. In particular, there is a possibly integrable regime with intermediate global symmetries, where the model is neither free bosons nor free fermions, but shows Poisson LSS in each global symmetry charge sector. This implies the existence of hidden (quasi)local conserved quantities. When the global symmetries are further lowered, the LSS in each charge sector becomes Wigner-Dyson, implying quantum chaos.We study a generic one-dimensonal quantum model of two flavors (pseudospins) chiral complex fermions by exact diagonalization, which can have local interflavor interaction and superconducting pairings (with all irrelevant terms ignored). Analytically, the model has two solvable (integrable) points in the parameter space: it is a free fermion model when the fermion interaction is zero, and is a free boson Luttinger liquid when there is a global U(1)$^{(\uparrow)}\times$U(1)$^{(\downarrow)}$ symmetry (with nonzero interaction). When the global symmetry of the interacting model is lowered by turning on symmetry breaking parameters, the model undergoes a transition from a quantum integrable model to a fully quantum chaotic model, as we demonstrate by examining the level spacing statistics (LSS) of the many-body energy spectrum. In particular, there is a possibly integrable regime with intermediate global symmetries, where the model is neither free bosons nor free fermions, but shows Poisson LSS in each global symmetry charge sector. This implies the existence of hidden (quasi)local conserved quantities. When the global symmetries are further lowered, the LSS in each charge sector becomes Wigner-Dyson, implying quantum chaos.

arXiv:2202.06169WORLD SCIENTIFIC eBooksSep 7, 20221 citation

^{(\uparrow)}\times

U(1)

^{(\downarrow)}

symmetry (with nonzero interaction). When the global symmetry of the interacting model is lowered by turning on symmetry breaking parameters, the model undergoes a transition from a quantum integrable model to a fully quantum chaotic model, as we demonstrate by examining the level spacing statistics (LSS) of the many-body energy spectrum. In particular, there is a possibly integrable regime with intermediate global symmetries, where the model is neither free bosons nor free fermions, but shows Poisson LSS in each global symmetry charge sector. This implies the existence of hidden (quasi)local conserved quantities. When the global symmetries are further lowered, the LSS in each charge sector becomes Wigner-Dyson, implying quantum chaos.