Memory effects in the relaxation of the Gaussian trap model

TL;DR

This paper studies the Kovacs memory effect in a Gaussian trap model for glassy relaxation, showing it occurs beyond linear response and analyzing its characteristics during temperature jumps.

Contribution

It demonstrates the presence of the Kovacs effect in a Gaussian trap model with finite-temperature equilibrium, including non-linear regimes and inverted temperature protocols.

Findings

Kovacs hump can be approximated as a difference of two decaying functions.

The effect persists beyond linear response regimes.

Inverted temperature jumps produce similar but sign-opposite Kovacs effects.

Abstract

We investigate the memory effect in a simple model for glassy relaxation, a trap model with a Gaussian density of states. In this model thermal equilibrium is reached at all finite temperatures and therefore we can consider jumps from low to high temperatures in addition to the quenches usually considered in aging studies. We show that the evolution of the energy following the Kovacs-protocol can approximately be expressed as a difference of two monotonously decaying functions and thus show the existence of a so-called Kovacs hump whenever these functions are not single exponentials. It is well established that the Kovacs effect also occurs in the linear response regime and we show that most of the gross features do not change dramatically when large temperature jumps are considered. However, there is one distinguishing feature that only exists beyond the linear regime which we discuss in detail. For the memory experiment with 'inverted' temperatures, i.e. jumping up and then down again, we find a very similar behavior apart from an opposite sign of the hump.