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

TL;DR

This paper investigates how off-diagonal disorder in a one-dimensional quantum system influences transmission properties, revealing the effects of microscopic randomness and establishing a large deviations principle for the transmission coefficient.

Contribution

It introduces a novel approach to analyze the asymptotic behavior of transmission in disordered quantum systems with fixed total barrier width.

Findings

Disorder affects the transmission coefficient significantly.

Fluctuations around regular lattice solutions are characterized.

Large deviations principle for transmission coefficient is established.

Abstract

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.