Transport through waveguides with surface disorder

TL;DR

This paper demonstrates that the conductance distribution in waveguides with surface disorder can be accurately modeled using the DMPK equation with direct processes, validated through numerical solutions for single-channel systems.

Contribution

It introduces a formulation incorporating direct processes into the DMPK equation for surface-disordered waveguides, with explicit calculations and numerical validation for the one-channel case.

Findings

DMPK equation with direct processes accurately models conductance distribution.

Numerical R-matrix solutions agree with the theoretical model.

Explicit single-channel calculations demonstrate the approach's validity.

Abstract

We show that the distribution of the conductance in quasi-one-dimensional systems with surface disorder is correctly described by the Dorokhov-Mello-Pereyra-Kumar equation if one includes direct processes in the scattering matrix S through Poisson's kernel. Although our formulation is valid for any arbitrary number of channels, we present explicit calculations in the one channel case. Ours result is compared with solutions of the Schroedinger equation for waveguides with surface disorder calculated numerically using the R-matrix method.