Derivation of fluctuating hydrodynamics and crossover from diffusive to anomalous transport in a hard-particle gas

TL;DR

This paper derives explicit microscopic expressions for diffusion and noise in a 1D hard-particle gas, explaining the crossover from diffusive to anomalous energy transport and confirming predictions numerically.

Contribution

It provides the first microscopic derivation of hydrodynamic equations and crossover length in a 1D gas model, connecting microscopic parameters to macroscopic transport behavior.

Findings

Energy current scales as L^{-2/3} with system size.

Crossover length from diffusive to anomalous transport is explicitly calculated.

Numerical verification confirms theoretical predictions.

Abstract

A recently developed non-linear fluctuating hydrodynamics theory has been quite successful in describing various features of anomalous energy transport. However the diffusion and the noise terms present in this theory are not derived from microscopic descriptions but rather added phenomenologically. We here derive these hydrodynamic equations with explicit calculation of the diffusion and noise terms in a one-dimensional model. We show that in this model the energy current scales anomalously with system size $L$ as $\sim L^{-2/3}$ in the leading order with a diffusive correction of order $\sim L^{-1}$. The crossover length $\ell_{c}$ from diffusive to anomalous transport is expressed in terms of microscopic parameters. Our theoretical predictions are verified numerically.