Statistics of Resonances in One Dimensional Continuous Systems

TL;DR

This paper derives an integral formula for the average density of resonances in a disordered one-dimensional continuous system with a random potential, providing insights into resonance behavior in open quantum systems.

Contribution

It introduces a novel integral representation for the density of resonances involving the wave function's logarithmic derivative in disordered continuous systems.

Findings

Derived an integral formula for the density of resonances.

Connected the density of resonances to the probability distribution of the wave function's logarithmic derivative.

Enhanced understanding of resonance statistics in disordered quantum systems.

Abstract

We study the average density of resonances (DOR) of a disordered one-dimensional continuous open system. The disordered system is semi-infinite, with white-noise random potential, and it is coupled to the external world by a semi-infinite continuous perfect lead. Our main result is an integral representation for the DOR which involves the probability density function of the logarithmic derivative of the wave function at the contact point.