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We study the transmission of a disordered waveguide subjected to a finitebias field. The statisticaldistribution of transmission is analytically shownto take a universal form. It depends on a singleparameter, the system lengthexpressed in a rescaled metrics, which encapsulates all the microscopicfeaturesof the medium and the bias field. Excellent agreement with numerics is foundfor variousmodels of disorder and bias field. For white-noise disorder and alinear bias field, we demonstratethe algebraic nature of the decay of thetransmission with distance, irrespective of the value ofthe bias field. Itcontrasts with the expansion of a wave packet, which features adelocalizationtransition for large bias field. The difference is attributed tothe different boundary conditionsfor the transmission and expansion schemes.The observability of these effects in conductancemeasurements for electrons orultracold atoms is discussed, taking into account key features, suchasfinite-range disorder correlations, nonlinear bias fields, and finitetemperatures.

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