Semiclassical Theory of Quantum Stochastic Resistors

We devise a semiclassical model to describe the transport properties of low-dimensional fermionic lattices under the influence of external quantum stochastic noise. These systems behave as quantum stochastic resistors, where the bulk particle transport is diffusive and obeys the Ohm/Fick's law. Here, we extend previous exact studies beyond the one-dimensional limit to ladder geometries and explore different dephasing mechanisms that are relevant to different physical systems, from solid-state to cold atoms. We show how the semiclassical description is useful to explain the nontrivial dependence of the conductance of these systems on the chemical potential of the reservoirs. This description provides an intuitive and simpler interpretation of transport in quantum stochastic resistors in good quantitative agreement with the exact numerical solution. Moreover, we find that the conductance of quantum ladders is insensitive to the coherence of the dephasing process along the direction transverse to transport, despite the fact that the system reaches different stationary states.