Occupation Time Statistics in the Quenched Trap Model

Abstract

We investigate the distribution of occupation times for a particle undergoing a random walk among random energy traps and in the presence of a deterministic potential field $U^{\det }(x)$. When the distribution of energy traps is exponential with a width $T_g$ we find that the occupation time statistics behaves according to (i) the canonical Boltzmann theory when $T>T_g$, (ii) while for $T<T_g$ they are distributed according to the Lamperti distribution with the asymmetry of the distribution determined by the Boltzmann factor $\exp (-U^{\det }(x)/T_g)$ with $T_g$ and not $T$ being the effective temperature. We explain how our results describe occupation times in other systems with quenched disorder, when the underlying partition function of the problem is a random variable distributed according to Lévy statistics.

5 pages, 2 figures

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