Thermalization in asymmetric harmonic chains

TL;DR

This paper explores how asymmetry in interparticle interactions influences thermalization in one-dimensional harmonic chains, revealing a power-law relationship and the distinct role of asymmetry in relaxation dynamics.

Contribution

It introduces an asymmetric harmonic model to isolate the effect of asymmetry on thermalization, and studies its interplay with nonlinearity, providing new insights into relaxation processes.

Findings

Thermalization time follows a power-law with perturbation strength.

Asymmetry enhances higher-order effects in relaxation.

Matthiessen's rule estimates thermalization time when nonlinearity is added.

Abstract

The symmetry of the interparticle interaction potential (IIP) plays a critical role in determining the thermodynamic and transport properties of solids. This study investigates the isolated effect of IIP asymmetry on thermalization. Asymmetry and nonlinearity are typically intertwined. To isolate the effect of asymmetry, we introduce a one-dimensional asymmetric harmonic (AH) model whose IIP possesses asymmetry but no nonlinearity, evidenced by energy-independent vibrational frequencies. Extensive numerical simulations confirm a power-law relationship between thermalization time ($T_{\rm eq}$) and perturbation strength for the AH chain, revealing an exponent larger than the previously observed inverse-square law in the thermodynamic limit. Upon adding symmetric quartic nonlinearity into the AH model, we systematically study thermalization under combined asymmetry and nonlinearity. Matthiessen's rule provides a good estimate of $T_{\rm eq}$ in this case. Our results demonstrate that asymmetry plays a distinct role in enhancing higher-order effects and governing relaxation dynamics.