Memory of the Initial Conditions in an Incompletely-Chaotic Quantum System: Universal Predictions and an Application to Cold Atoms

TL;DR

This paper investigates how initial conditions influence the long-term behavior of a quantum system transitioning from integrability to chaos, providing universal predictions validated through cold atom experiments.

Contribution

It introduces a universal law describing the relaxation of observables in quantum systems with no selection rules, bridging integrable and chaotic regimes.

Findings

Universal linear interpolation law for observable relaxation

Validation with cold atom waveguide experiments

Robust across various initial states and interaction strengths

Abstract

Two zero-range-interacting atoms in a circular, transversely harmonic waveguide are used as a test-bench for a quantitative description of the crossover between integrability and chaos in a quantum system with no selection rules. For such systems we show that the expectation value after relaxation of a generic observable is given by a linear interpolation between its initial and thermal expectation values. The variable of this interpolation is universal; it governs this simple law to cover the whole spectrum of the chaotic behavior from integrable regime through the well- developed quantum chaos. The predictions are confirmed for the waveguide system, where the mode occupations and the trapping energy were used as the observables of interest; a variety of the initial states and a full range of the interaction strengths have been tested.