Quantum Recurrences in a One-Dimensional Gas of Impenetrable Bosons

TL;DR

This paper investigates quantum recurrence phenomena in a 1D gas of impenetrable bosons, demonstrating how single-particle recurrences lead to gas state recurrences, with implications for understanding thermalization and recurrence in quantum many-body systems.

Contribution

It provides an exact analysis of quantum recurrences in a 1D Bose gas, linking single-particle dynamics to many-body recurrence phenomena and discussing implications for quantum thermalization.

Findings

Single-particle states recur in a 1D box, showing back-and-forth motion.

The entire gas state can recur if particles start in the same momentum superposition.

Estimated recurrence times align with experimental observations in cold atom systems.

Abstract

It is well-known that a dilute one-dimensional (1D) gas of bosons with infinitely strong repulsive interactions behaves like a gas of free fermions. Just as with conduction electrons in metals, we consider a single-particle picture of the resulting dynamics, when the gas is isolated by enclosing it into a box with hard walls and preparing it in a special initial state. We show, by solving the nonstationary problem of a free particle in a 1D hard-wall box, that the single-particle state recurs in time, signaling the intuitively expected back-and-forth motion of a free particle moving in a confined space. Under suitable conditions, the state of the whole gas can then be made to recur if all the particles are put in the same initial momentum superposition. We introduce this problem here as a modern instance of the discussions giving rise to the famous recurrence paradox in statistical mechanics: on one hand, our results may be used to develop a poor man's interpretation of the recurrence of the initial state observed [T. Kinoshita et al, Nature 440, 900 (2006)] in trapped 1D Bose gases of cold atoms, for which our estimated recurrence time is in fair agreement with the period of the oscillations observed; but this experiment, on the other hand, has been substantially influential on the belief that an isolated quantum many-body system can equilibrate as a consequence of its own unitary nonequilibrium dynamics. Some ideas regarding the latter are discussed.