  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, while their total width is kept constant. 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
deviations principle for the transmission coefficient.
