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

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.

5 pages, 5 figures + 4 pages, 4 figures; new result on entropy production and viscous correction, new appendix

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