Current in a quantum driven thermostatted system with off-diagonal disorder

We analyze a one dimensional quantum model with off-diagonal disorder, consisting of a sequence of potential energy barriers whose width is a random variable either uniformly or “half-normally” distributed, subjected to an external electric field. We shed light on how the microscopic disorder affects the value of the transmission coefficient and on the structure of the fluctuations around the solutions corresponding to the regular lattice configuration. We also characterize the asymptotic limit obtained by letting the number of barriers diverge. Thus, we explain the novelty of our method with respect to the standard thermodynamic limit discussed in the literature and also evidence the onset of a large deviation principle for the transmission coefficient.