Non-stationary heat conduction in one-dimensional chains with conserved momentum

TL;DR

This paper investigates non-stationary heat conduction in one-dimensional models with conserved momentum, revealing a crossover from oscillatory to diffusive decay that challenges classical Fourier-based descriptions.

Contribution

It demonstrates that hyperbolic heat conduction models are insufficient for these systems, highlighting the need for alternative descriptions of non-stationary heat transfer in such chains.

Findings

Crossover from oscillatory to diffusive decay observed

Behavior inconsistent with classical Fourier heat conduction

Hyperbolic models like Cattaneo-Vernotte are inadequate

Abstract

The Letter addresses the relationship between hyperbolic equations of heat conduction and microscopic models of dielectrics. Effects of the non-stationary heat conduction are investigated in two one-dimensional models with conserved momentum: Fermi-Pasta-Ulam (FPU) chain and chain of rotators (CR). These models belong to different universality classes with respect to stationary heat conduction. Direct numeric simulations reveal in both models a crossover from oscillatory decay of short-wave perturbations of the temperature field to smooth diffusive decay of the long-wave perturbations. Such behavior is inconsistent with parabolic Fourier equation of the heat conduction. The crossover wavelength decreases with increase of average temperature in both models. For the FPU model the lowest order hyperbolic Cattaneo-Vernotte equation for the non-stationary heat conduction is not applicable, since no unique relaxation time can be determined.