An Exactly Solvable Model for the Integrability-Chaos Transition in Rough Quantum Billiards

Abstract

A central question of dynamics, largely open in the quantum case, is to what extent it erases a system's memory of its initial properties. Here we present a simple statistically solvable quantum model describing this memory loss across an integrability-chaos transition under a perturbation obeying no selection rules. From the perspective of quantum localization-delocalization on the lattice of quantum numbers, we are dealing with a situation where every lattice site is coupled to every other site with the same strength, on average. The model also rigorously justifies a similar set of relationships recently proposed in the context of two short-range-interacting ultracold atoms in a harmonic waveguide. Application of our model to an ensemble of uncorrelated impurities on a rectangular lattice gives good agreement with ab initio numerics.

29 pages, 5 figures

References in corpus (8)

• Thermalization and its mechanism for generic isolated quantum systems
• Direct observation of Anderson localization of matter-waves in a controlled disorder
• Probing the relaxation towards equilibrium in an isolated strongly correlated 1D Bose gas
• Non-equilibrium coherence dynamics in one-dimensional Bose gases
• Breakdown of thermalization in finite one-dimensional systems
• The Luttinger model following a sudden interaction switch-on
• Quasi-one-dimensional scattering in a discrete model
• The mesoscopic conductance of disordered rings, its random matrix theory, and the generalized variable range hopping picture

Cited by in corpus (19)

• Relaxation and Pre-thermalization in an Isolated Quantum System
• From Bloch Oscillations to Many Body Localization in Clean Interacting Systems
• Typical fast thermalization processes in closed many-body systems
• Glimmers of a Quantum KAM Theorem: Insights from Quantum Quenches in One Dimensional Bose Gases
• Chaos-driven dynamics in spin-orbit coupled atomic gases
• Eigenstate Gibbs Ensemble in Integrable Quantum Systems
• Exponentially fast dynamics of chaotic many-body systems
• Quantum XX-model with competing short- and long-range interactions: Phases and phase transitions in and out of equilibrium
• Relaxation of the order-parameter statistics in the Ising quantum chain
• Krylov fractality and complexity in generic random matrix ensembles
• Geometry of quantum observables and thermodynamics of small systems
• Superfluidity in Bose-Hubbard circuits
• Entanglement witnesses in the XY chain: Thermal equilibrium and postquench nonequilibrium states
• Eigenstates of Thiophosgene Near the Dissociation Threshold -- Deviations From Ergodicity
• Semiclassical theory of strong localization for quantum thermalization
• Exploring integrability-chaos transition with a sequence of independent perturbations
• Unitary work extraction from a Generalized Gibbs Ensemble using Bragg scattering
• Entanglement production by statistical operators
• Quantum chaos in a harmonic waveguide with scatterers