Diffraction induced quantum chaos in a one-dimensional Bose gas

TL;DR

This paper studies how a localized impurity in a one-dimensional Bose gas causes a transition from integrability to quantum chaos, with low-energy spectral statistics showing unexpected chaotic behavior contrary to typical high-energy emergence.

Contribution

It demonstrates that a delta impurity induces quantum chaos in the Lieb--Liniger model at low energies, challenging conventional beliefs about chaos onset in quantum systems.

Findings

Low-energy spectrum exhibits random-matrix statistics.

Odd-parity sector remains integrable for two bosons.

Both sectors show chaos at low energy for three bosons.

Abstract

We investigate the Lieb--Liniger model of interacting one-dimensional bosons coupled to a localized impurity, modeled by a delta barrier. While the Lieb--Liniger gas is integrable, the impurity breaks integrability and induces a transition towards quantum chaos. We show that the low-energy spectrum exhibits random-matrix statistics, in striking contrast to the Bohigas--Giannoni--Schmit conjecture, where chaotic behavior typically emerges at high energy. For two bosons, the odd-parity sector remains integrable, whereas the even-parity sector displays clear signatures of chaos at low energy and a crossover back to quasi-integrable behavior at higher energies. For three bosons, both parity sectors exhibit spectral statistics close to chaos at low energy. We argue that this unconventional form of few-body quantum chaos originates from diffractive processes induced by the impurity.