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

We study the transmission of a disordered waveguide subjected to a finite bias field. The statistical distribution of transmission is analytically shown to take a universal form. It depends on a single parameter, the system length expressed in a rescaled metrics, which encapsulates all the microscopic features of the medium and the bias field. Excellent agreement with numerics is found for various models of disorder and bias field. For white-noise disorder 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 a delocalization transition for large bias field. The difference is attributed to the different boundary conditions for the transmission and expansion schemes. The observability of these effects in conductance measurements for electrons or ultracold atoms is discussed, taking into account key features, such as finite-range disorder correlations, nonlinear bias fields, and finite temperatures.