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We investigate ergodicity, chaos and thermalization for a one-dimensionalclassical gas of hard rods confined to an external quadratic or quartic trap,which breaks microscopic integrability. To quantify the strength of chaos inthis system, we compute its maximal Lyapunov exponent numerically. The approachto thermal equilibrium is studied by considering the time evolution of particleposition and velocity distributions and comparing the late-time profiles withthe Gibbs state. Remarkably, we find that quadratically trapped hard rods arehighly non-ergodic and do not resemble a Gibbs state even at extremely longtimes, despite compelling evidence of chaos for four or more rods. On the otherhand, our numerical results reveal that hard rods in a quartic trap exhibitboth chaos and thermalization, and equilibrate to a Gibbs state as expected fora nonintegrable many-body system.

Unusual ergodic and chaotic properties of trapped hard rods