Scaling properties of delay times in one-dimensional random media

TL;DR

This paper investigates how the inverse moments of Wigner delay times scale in finite 1D random media, revealing a universal law independent of microscopic details, supported by numerical evidence across various physical systems.

Contribution

It introduces a universal scaling law for inverse moments of Wigner delay times in 1D random media, confirmed through numerical simulations.

Findings

Inverse moments follow a simple, universal scaling law.

The scaling law is independent of microscopic details.

Numerical validation across diverse physical systems.

Abstract

The scaling properties of the inverse moments of Wigner delay times are investigated in finite one-dimensional (1D) random media with one channel attached to the boundary of the sample. We find that they follow a simple scaling law which is independent of the microscopic details of the random potential. Our theoretical considerations are confirmed numerically for systems as diverse as 1D disordered wires and optical lattices to microwave waveguides with correlated scatterers.