Nonlinear fluctuating hydrodynamics for anharmonic chains

TL;DR

This paper develops a nonlinear fluctuating hydrodynamics framework for anharmonic chains, enabling rapid computation of model parameters and providing detailed predictions for equilibrium correlations in one-dimensional systems.

Contribution

It introduces a second-order nonlinear fluctuating hydrodynamics model with a practical parameter computation method applicable to any 1D local conservation law system.

Findings

Provides analytical large-scale predictions for correlation functions.

Offers a numerical approach for parameter calculation within seconds.

Validates predictions through numerical simulations of mode-coupling equations.

Abstract

With focus on anharmonic chains, we develop a nonlinear version of fluctuating hydrodynamics, in which the Euler currents are kept to second order in the deviations from equilibrium and dissipation plus noise are added. The required model-dependent parameters are written in such a way that they can be computed numerically within seconds, once the interaction potential, pressure, and temperature are given. In principle the theory is applicable to any one-dimensional system with local conservation laws. The resulting nonlinear stochastic field theory is handled in the one-loop approximation. Some of the large scale predictions can still be worked out analytically. For more details one has to rely on numerical simulations of the corresponding mode-coupling equations. In this way we arrive at detailed predictions for the equilibrium time correlations of the locally conserved fields of an anharmonic chain.