Quasiparticle dynamics and diffusive scale hydrodynamics in an inhomogeneous gas of hard rods

Abstract

We investigate the stochastic dynamics of quasiparticles within a gas of hard rods in one dimension for two choices of initial states: one with long-range correlations and the other without it. We derive analytical results for the phase space density correlations in the former case to complement the known results for the latter case. These results enable us to obtain explicit expressions for the mean, variance, autocorrelation and cross-correlation of individual quasiparticles, extending previous results to inhomogeneous cases. We also propose two methods for simulating an ensemble of trajectories of a quasiparticle with fixed initial position and velocity, and verify our analytical results on correlations. The long-range correlations introduce a diffusive-scale correction to the mean Euler generalized hydrodynamic equations, modifying the standard local equilibrium form, and our findings reveal that the form of the correction term depends on the long-range correlations present in the system.

33 pages