Occupation time statistics in the quenched trap model

We investigate the distribution of the occupation time of a particle undergoing a random walk among random energy traps and in the presence of a deterministic potential field. When the distribution of energy traps is exponential with a width T-g, we find in thermal equilibrium a transition between Boltzmann statistics when T > T-g to Lamperti statistics when T < T-g. We explain why our main results are valid for other models of quenched disorder, and discuss briefly implications on single particle experiments.