Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2009-11-20
J. Stat. Mech. (2010) P02009
Physics
Condensed Matter
Statistical Mechanics
Accepted version in JSTAT, minor changes, some errata fixed; 30 pages, 8 figures
Scientific paper
10.1088/1742-5468/2010/02/P02009
The Kovacs or crossover effect is one of the peculiar behaviours exhibited by glasses and other complex, slowly relaxing systems. Roughly it consists in the non-monotonic relaxation to its equilibrium value of a macroscopic property of a system evolving at constant temperature, when starting from a non-equilibrium state. Here, this effect is investigated for general systems whose dynamics is described by a master equation. To carry out a detailed analysis, the limit of small perturbations in which linear response theory applies is considered. It is shown that, under very general conditions, the observed experimental features of the Kovacs effect are recovered. The results are particularized for a very simple model, a two-level system with dynamical disorder. An explicit analytical expression for its non-monotonic relaxation function is obtained, showing a resonant-like behaviour when the dependence on the temperature is investigated.
Brey Javier J.
Prados Ana
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