The response of jammed packings to thermal fluctuations

TL;DR

This study investigates how thermal fluctuations influence the nonlinear response of jammed packings of frictionless disks, identifying the temperature thresholds for contact breaking and analyzing the effects on system properties.

Contribution

It quantifies the impact of contact-breaking nonlinearities and distinguishes their effects from form nonlinearities in thermal responses of jammed packings.

Findings

Deviation in specific heat grows rapidly above contact-breaking temperature

Deviation decreases with increasing system size as N^{-1}

Contact-breaking nonlinearities dominate over form nonlinearities for linear springs

Abstract

We focus on the response of mechanically stable (MS) packings of frictionless, bidisperse disks to thermal fluctuations, with the aim of quantifying how nonlinearities affect system properties at finite temperature. Packings of disks with purely repulsive contact interactions possess two main types of nonlinearities, one from the form of the interaction potential and one from the breaking (or forming) of interparticle contacts. To identify the temperature regime at which the contact-breaking nonlinearities begin to contribute, we first calculated the minimum temperatures $T_{cb}$ required to break a single contact in the MS packing for both single and multiple eigenmode perturbations of the $T=0$ MS packing. We then studied deviations in the constant volume specific heat $C_V$ and deviations of the average disk positions $\Delta r$ from their $T=0$ values in the temperature regime $T_{cb} < T < T_{r}$, where $T_r$ is the temperature beyond which the system samples the basin of a new MS packing. We find that the deviation in the specific heat per particle $\Delta {\overline C}_V^0/{\overline C}_V^0$ relative to the zero temperature value ${\overline C}_V^0$ can grow rapidly above $T_{cb}$, however, the deviation $\Delta {\overline C}_V^0/{\overline C}_V^0$ decreases as $N^{-1}$ with increasing system size. To characterize the relative strength of contact-breaking versus form nonlinearities, we measured the ratio of the average position deviations $\Delta r^{ss}/\Delta r^{ds}$ for single- and double-sided linear and nonlinear spring interactions. We find that $\Delta r^{ss}/\Delta r^{ds} > 100$ for linear spring interactions and is independent of system size.