Unusual ergodic and chaotic properties of trapped hard rods

TL;DR

This study explores how one-dimensional hard rods in quadratic and quartic traps exhibit different ergodic and chaotic behaviors, with quadratic traps showing non-ergodicity and quartic traps achieving thermalization.

Contribution

It demonstrates that quadratic traps prevent ergodicity despite chaos, while quartic traps enable thermalization, highlighting the impact of external potential shape on many-body dynamics.

Findings

Quadratic traps lead to non-ergodic behavior even with chaos.

Quartic traps facilitate thermalization and Gibbs state formation.

Chaos is present in systems with four or more rods.

Abstract

We investigate ergodicity, chaos and thermalization for a one-dimensional classical gas of hard rods confined to an external quadratic or quartic trap, which breaks microscopic integrability. To quantify the strength of chaos in this system, we compute its maximal Lyapunov exponent numerically. The approach to thermal equilibrium is studied by considering the time evolution of particle position and velocity distributions and comparing the late-time profiles with the Gibbs state. Remarkably, we find that quadratically trapped hard rods are highly non-ergodic and do not resemble a Gibbs state even at extremely long times, despite compelling evidence of chaos for four or more rods. On the other hand, our numerical results reveal that hard rods in a quartic trap exhibit both chaos and thermalization, and equilibrate to a Gibbs state as expected for a nonintegrable many-body system.