Abstract
We investigate diffusion of a quantum charged particle in a tight-binding lattice (TBL) under fluctuating noisy electric fields. Several closed-form expressions such as that of probability propagator, average current, and mean-squared displacement are derived. The particular effect of Gaussian noise in a 1D TBL is studied in detail and a comparison is made with the case of a telegraph noise. The Gaussian white noise and telegraph noise show up in different manifestations in the underdamped regime. On the contrary, when relaxation is rapid the noisy field averages out to zero yielding delocalization for both Gaussian and telegraphic noisy electric fields. Depending on the strength of noise and the external field one can observe different current characteristics.
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