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Occupation Time Statistics in the Quenched Trap Model

S. Burov·E. Barkai
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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 $U^{\rm det}(x)$. 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 $\exp(-U^{\rm det}(x)/T_g)$ 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.

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S. Burov, E. Barkai. 2006-12-28. Occupation Time Statistics in the Quenched Trap Model. https://doi.org/10.1103/physrevlett.98.250601

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