Fingerprints of classical diffusion in open 2D mesoscopic systems in the metallic regime

TL;DR

This paper explores how classical diffusion influences quantum scattering properties in open 2D mesoscopic systems within the metallic regime, revealing characteristic distribution patterns linked to classical dynamics.

Contribution

It provides a detailed analysis of resonance width and delay time distributions in diffusive 2D systems, connecting quantum scattering features with classical diffusion behavior.

Findings

Distribution of resonance widths follows a power law in certain regimes.

Wigner delay times exhibit a log-normal distribution for large values.

Classical diffusive dynamics determine the quantum scattering distributions.

Abstract

We investigate the distribution of the resonance widths ${\cal P}(\Gamma)$ and Wigner delay times ${\cal P}(\tau_W)$ for scattering from two-dimensional systems in the diffusive regime. We obtain the forms of these distributions (log-normal for large $\tau_W$ and small $\Gamma$, and power law in the opposite case) for different symmetry classes and show that they are determined by the underlying diffusive classical dynamics. Our theoretical arguments are supported by extensive numerical calculations.