# Thermalization in Asymmetric Harmonic Chains

## TL;DR

This paper studies how asymmetry in particle interactions affects thermalization in solids, showing that asymmetry enhances relaxation dynamics differently than nonlinearity.

## Contribution

The study introduces a one-dimensional asymmetric harmonic model to isolate the effect of asymmetry on thermalization.

## Key findings

- Thermalization time follows a power-law with an exponent larger than the inverse-square law in the thermodynamic limit.
- Matthiessen’s rule accurately estimates thermalization time when asymmetry and nonlinearity are combined.
- Asymmetry enhances higher-order effects and governs relaxation dynamics distinct from nonlinearity.

## 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 (Teq) 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 Teq in this case. Our results demonstrate that asymmetry plays a distinct role in enhancing higher-order effects and governing relaxation dynamics.