Irregular Dynamics in a One-Dimensional Bose System

TL;DR

This paper investigates the transition from regular to chaotic quantum dynamics in a one-dimensional Bose system, revealing how interactions influence entropy, momentum distribution, and relaxation behavior, with implications for experimental observation.

Contribution

It provides a combined analytical and numerical analysis of the dynamical transition from mean-field to Tonks-Girardeau regimes in 1D bosons, linking chaos onset to observable momentum distribution changes.

Findings

Transition from regular to chaotic dynamics coincides with Tonks-Girardeau regime onset

Momentum distribution shows statistical relaxation in the strongly interacting regime

Transition observable through interference fringes after trap release

Abstract

We study many-body quantum dynamics of $\delta$-interacting bosons confined in a one-dimensional ring. Main attention is payed to the transition from the mean-field to Tonks-Girardeau regime using an approach developed in the theory of interacting particles. We analyze, both analytically and numerically, how the Shannon entropy of the wavefunction and the momentum distribution depend on time for a weak and strong interactions. We show that the transition from regular (quasi-periodic) to irregular ("chaotic") dynamics coincides with the onset of the Tonks-Girardeau regime. In the latter regime the momentum distribution of the system reveals a statistical relaxation to a steady state distribution. The transition can be observed experimentally by studying the interference fringes obtained after releasing the trap and letting the boson system expand ballistically.