Laurent Sanchez-Palencia

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

We study the transmission and conductance of a disordered matter wave guide subjected to a finite bias force field. We show that the statistical distribution of transmission takes a universal form. This distribution depends on a single parameter, the system length expressed in a rescaled metrics, which encapsulates all the microscopic features of the medium. Excellent agreement with numerics is found for various models of disorder and bias. For white-noise disorder and a constant force, we find algebraic decay of the transmission with distance, irrespective of the value of the force. The observability of these effects in ultracold atomic gases is discussed, taking into account specific features, such as finite-range disorder correlations, inhomogeneous forces, and finite temperatures.

Expansion of a quantum wave packet in a one-dimensional disordered potential in the presence of a uniform bias force

We study numerically the expansion dynamics of an initially confined quantum wave packet in the presence of a disordered potential and a uniform bias force. For white-noise disorder, we find that the wave packet develops asymmetric algebraic tails for any ratio of the force to the disorder strength. The exponent of the algebraic tails decays smoothly with that ratio and no evidence of a critical behavior on the wave density profile is found. Algebraic localization features a series of critical values of the force-to-disorder strength where the m-th position moment of the wave packet diverges. Below the critical value for the m-th moment, we find fair agreement between the asymptotic long-time value of the m-th moment and the predictions of diagrammatic calculations. Above it, we find that the m-th moment grows algebraically in time. For correlated disorder, we find evidence of systematic delocalization, irrespective to the model of disorder. More precisely, we find a two-step dynamics, where both the center-of-mass position and the width of the wave packet show transient localization, similar to the white-noise case, at short time and delocalization at sufficiently long time. This correlation-induced delocalization is interpreted as due to the decrease of the effective de Broglie wave length, which lowers the effective strength of the disorder in the presence of finite-range correlations.