Time Delay Correlations and Resonances in 1D Disordered Systems

TL;DR

This paper analytically studies the frequency-dependent time delay correlation function in 1D disordered systems, revealing algebraic decay behaviors and connecting it to resonance width distributions, supported by numerical simulations.

Contribution

It introduces an analytical framework linking time delay correlations to resonance widths in 1D disordered systems, supported by numerical validation.

Findings

Both $K(\Omega)$ and $ ho(\Gamma)$ decay algebraically with exponent ~1.25.

Analytical formulas match numerical results in 1D non-Hermitian models.

Resonance width distribution can be extracted from time delay correlations.

Abstract

The frequency dependent time delay correlation function $K(\Omega)$ is studied analytically for a particle reflected from a finite one-dimensional disordered system. In the long sample limit $K(\Omega)$ can be used to extract the resonance width distribution $\rho(\Gamma)$. Both quantities are found to decay algebraically as $\Gamma^{-\nu}$, and $\Omega^{-\nu}$, $\nu\simeq 1.25$ in a large range of arguments. Numerical calculations for the resonance width distribution in 1D non-Hermitian tight-binding model agree reasonably with the analytical formulas.