Unusual ergodic and chaotic properties of trapped hard 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.

10 pages, 10 figures

References in corpus (6)

• Physics and Mathematics of Calogero particles
• Generalized hydrodynamics in strongly interacting 1D Bose gases
• Thermalisation of a trapped one-dimensional Bose gas via diffusion
• On Classical Integrability of the Hydrodynamics of Quantum Integrable Systems
• Transport properties of the classical Toda chain: effect of a pinning potential
• Finite temperature equilibrium density profiles of integrable systems in confining potentials

Cited by in corpus (6)

• Probing the local rapidity distribution of a 1D Bose gas
• Diffusive hydrodynamics from long-range correlations
• Revised Enskog equation for hard rods
• Identifying diffusive length scales in one-dimensional Bose gases
• Simulating generalised fluids via interacting wave packets evolution
• Diffusive hydrodynamics of hard rods from microscopics