The statistics of Wigner delay time in Anderson disordered systems

TL;DR

This paper numerically studies the statistical distribution of Wigner delay times in Anderson disordered systems across different dimensions and symmetry classes, revealing universal power-law behaviors and the influence of necklace states.

Contribution

It uncovers universal power-law regimes in Wigner delay time distributions and links the second regime to necklace states, across various disordered systems and symmetry classes.

Findings

Distribution of delay times follows a universal pattern in 2D and QD systems.

Two distinct power-law regimes with exponents -1.5 and -2 were identified.

Necklace states are responsible for the rare second power-law behavior.

Abstract

We numerically investigate the statistical properties of Wigner delay time in Anderson disordered 1D, 2D and quantum dot (QD) systems. The distribution of proper delay time for each conducting channel is found to be universal in 2D and QD systems for all Dyson's symmetry classes and shows a piece-wise power law behavior in the strong localized regime. Two power law behaviors were identified with asymptotical scaling ${\tau^{-1.5}}$ and ${\tau^{-2}}$, respectively that are independent of the number of conducting channels and Dyson's symmetry class. Two power-law regimes are separated by the relevant time scale $\tau_0 \sim h/\Delta$ where $\Delta$ is the average level spacing. It is found that the existence of necklace states is responsible for the second power-law behavior ${\tau^{-2}}$, which has an extremely small distribution probability.