Effect of a bias field on disordered waveguides: Universal scaling of conductance and application to ultracold atoms

摘要

We study the transmission of a disordered waveguide subjected to a finite bias field. The statistical distributionof transmission is analytically shown to take a universal form. It depends on a single parameter, the system lengthexpressed in a rescaled metrics, which encapsulates all the microscopic features of the medium and the biasfield. Excellent agreement with numerics is found for various models of disorder and bias field. For white-noisedisorder and a linear bias field, we demonstrate the algebraic nature of the decay of the transmission with distance,irrespective of the value of the bias field. It contrasts with the expansion of a wave packet, which features adelocalization transition for large bias field. The difference is attributed to the different boundary conditionsfor the transmission and expansion schemes. The observability of these effects in conductance measurementsfor electrons or ultracold atoms is discussed, taking into account key features, such as finite-range disordercorrelations, nonlinear bias fields, and finite temperatures.