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

TL;DR

This paper analyzes how a bias field affects waveguide transmission, revealing a universal statistical form dependent on a rescaled system length, with implications for ultracold atoms and electronic conductance.

Contribution

It introduces a universal scaling law for transmission in biased disordered waveguides, validated across various models and applicable to ultracold atoms and electrons.

Findings

Universal transmission distribution depending on a single parameter

Algebraic decay of transmission with distance under linear bias

Contrast between transmission decay and wave packet expansion behaviors

Abstract

We study the transmission of a disordered waveguide subjected to a finite bias field. The statisticaldistribution of transmission is analytically shown to take a universal form. It depends on a singleparameter, the system length expressed in a rescaled metrics, which encapsulates all the microscopicfeatures of the medium and the bias field. Excellent agreement with numerics is found for variousmodels of disorder and bias field. For white-noise disorder and a linear bias field, we demonstratethe algebraic nature of the decay of the transmission with distance, irrespective of the value ofthe bias field. It contrasts with the expansion of a wave packet, which features a delocalizationtransition for large bias field. The difference is attributed to the different boundary conditionsfor the transmission and expansion schemes. The observability of these effects in conductancemeasurements for electrons or ultracold atoms is discussed, taking into account key features, suchas finite-range disorder correlations, nonlinear bias fields, and finite temperatures.