The Kovacs effect in model glasses

We discuss the 'memory effect' discovered in the 1960s by Kovacs in temperature shift experiments on glassy polymers, where the volume (or energy) displays a non-monotonic time behaviour. This effect is generic and is observed in a variety of different glassy systems (including granular materials). The aim of this paper is to discuss whether some microscopic information can be extracted from a quantitative analysis of the 'Kovacs hump'. We study analytically two families of theoretical models: domain growth and traps, for which detailed predictions of the shape of the hump can be obtained. Qualitatively, the Kovacs effect reflects the heterogeneity of the system: its description requires dealing not only with averages but with a full probability distribution (of domain sizes or of relaxation times). We conclude by some suggestions for a quantitative analysis of experimental results.