Incomplete thermalization from trap-induced integrability breaking: lessons from classical hard rods

TL;DR

This paper investigates how a harmonic trap induces incomplete thermalization in a one-dimensional gas of hard rods, revealing distinct dynamical regimes and the failure to reach thermal equilibrium within studied timescales.

Contribution

It demonstrates how trap-induced integrability breaking affects the dynamics and thermalization process of classical hard rods, highlighting regimes of chaos and stationarity.

Findings

System exhibits initial, chaotic, and stationary regimes.

Hydrodynamics breaks down for finite particles, leading to chaos.

System does not thermalize within the observed timescale.

Abstract

We study a one-dimensional gas of hard rods trapped in a harmonic potential, which breaks integrability of the hard-rod interaction in a non-uniform way. We explore the consequences of such broken integrability for the dynamics of a large number of particles and find three distinct regimes: initial, chaotic, and stationary. The initial regime is captured by an evolution equation for the phase-space distribution function. For any finite number of particles, this hydrodynamics breaks down and the dynamics become chaotic after a characteristic time scale determined by the inter-particle distance and scattering length. The system fails to thermalize over the time-scale studied ($10^4$ natural units), but the time-averaged ensemble is a stationary state of the hydrodynamic evolution. We close by discussing logical extensions of the results to similar systems of quantum particles.