Effective Forces in Thermal Amorphous Solids with Generic Interactions

TL;DR

This paper develops an effective theory for thermal amorphous solids with generic interactions, providing analytic expressions for effective forces and demonstrating their predictive power in understanding stable glassy systems.

Contribution

It introduces a new effective theory for thermal glasses with generic interactions, deriving effective forces from an effective potential and analyzing stability via an effective Hessian.

Findings

Effective forces can be derived from an effective potential in thermal glasses.

The effective Hessian's eigenvalues are positive for stable systems.

Analytic expressions enable predictions of system behavior.

Abstract

In thermal glasses at temperatures sufficiently lower than the glass transition, the constituent particles are trapped in their cages for sufficiently long time such that their {\em time-averaged positions} can be determined before diffusion and structural relaxation takes place. The effective forces are those that hold these average positions in place. In numerical simulations the effective forces $\B F_{ij}$ between any pair of particles can be measured as a time average of the {\em bare} forces $\B f_{ij}(\B r_{ij}(t))$. In general even if the bare forces come from two-body interactions, thermal dynamics dress the effective forces to contain many-body interactions. Here we develop the effective theory for systems with generic interactions, where the effective forces are derivable from an effective potential and in turn they give rise to an effective Hessian whose eigenvalues are all positive when the system is stable. In this Letter we offer analytic expressions for the effective theory, and demonstrate the usefulness and the predictive power of the approach.