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

TL;DR

This paper investigates how a quantum wave packet expands in a one-dimensional disordered potential with a bias force, revealing algebraic localization, critical force ratios, and delocalization effects due to disorder correlations.

Contribution

It provides a detailed numerical analysis of wave packet dynamics under disorder and bias, highlighting algebraic localization and correlation-induced delocalization phenomena.

Findings

Wave packet develops asymmetric algebraic tails for any force-to-disorder ratio.

Critical values of force-to-disorder strength cause divergence in wave packet moments.

Correlated disorder leads to systematic delocalization regardless of disorder model.

Abstract

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.