Fluctuating hydrodynamics approach to equilibrium time correlations for anharmonic chains

TL;DR

This paper extends fluctuating hydrodynamics to nonlinear regimes in one-dimensional anharmonic chains, addressing anomalous transport phenomena and validating the theory with molecular dynamics simulations.

Contribution

It develops a nonlinear fluctuating hydrodynamics framework for 1D anharmonic chains, capturing anomalous transport beyond linear approximations.

Findings

The nonlinear theory aligns well with molecular dynamics results.

Quadratic Euler currents are key to understanding anomalous transport.

The approach provides a mesoscopic description of 1D fluid systems.

Abstract

Linear fluctuating hydrodynamics is a useful and versatile tool for describing fluids, as well as other systems with conserved fields, on a mesoscopic scale. In one spatial dimension, however, transport is anomalous, which requires to develop a nonlinear extension of fluctuating hydrodynamics. The relevant nonlinearity turns out to be the quadratic part of the Euler currents when expanding relative to a uniform background. We outline the theory and compare with recent molecular dynamics simulations.