Statistical properties of phases and delay times of the one-dimensional Anderson model with one open channel

TL;DR

This paper analyzes the statistical distributions of phases and delay times in a one-dimensional Anderson model with a single open channel, revealing a transition in phase distribution and universal power-law tails in delay times.

Contribution

It provides an analytical approach using classical Hamiltonian maps to study phase and delay time distributions in the Anderson model, highlighting a transition based on disorder strength.

Findings

Phase distribution transitions from uniform to singular with increasing disorder parameter

Delay time distribution exhibits universal 1/τ^2 power law tails

Short time delay behavior depends on disorder parameter

Abstract

We study the distribution of phases and of Wigner delay times for a one-dimensional Anderson model with one open channel. Our approach, based on classical Hamiltonian maps, allows us an analytical treatment. We find that the distribution of phases depends drastically on the parameter $\sigma_A = \sigma/sin k$ where $\sigma^2$ is the variance of the disorder distribution and $k$ the wavevector. It undergoes a transition from uniformity to singular behaviour as $\sigma_A$ increases. The distribution of delay times shows universal power law tails $~ 1/\tau^2$, while the short time behaviour is $\sigma_A$- dependent.