1/fnoise in a hopping model with trapping

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Abstract
We consider a charge carrier executing a random walk on a lattice with trap states at each site. Each trap state has a release rate w and a trapping rate λw, where w and λ are independent quenched random variables. We solve the master equation formally for the fourth moment of the displacement of an unbiased walk and for the second moment of the displacement of a weakly biased walk. We show that the same function of the quenched disorder describes both quantities, and that this corresponds to an equivalence between equilibrium and nonequilibrium excess low-frequency noise. We carry out a low-frequency expansion of these moments when the hopping rates are large compared to the frequency and to the trapping rates. The leading term in this expansion is evaluated analytically and gives 1/f current noise when the logarithm of w has a broad distribution.