Parametric Correlations of Scattering Phase Shifts and Fluctuations of Delay Times in Few-Channel Chaotic Scattering

TL;DR

This paper derives explicit formulas for the correlations of eigenphase densities and delay times in chaotic quantum systems with broken time-reversal symmetry, enhancing understanding of their parametric fluctuations.

Contribution

It introduces a new supersymmetry-based method to explicitly compute parametric correlation functions of eigenphases and delay times in multi-channel chaotic scattering.

Findings

Derived explicit correlation functions for eigenphase densities

Obtained distribution of phase-shift derivatives over energy and parameters

Analyzed parametric correlations of Wigner-Smith delay times

Abstract

By using the supersymmetry method we derive an explicit expression for the parametric correlation function of densities of eigenphases $\theta_a$ of the S-matrix in a chaotic quantum system with broken time-reversal symmetry coupled to continua via M equivalent open channels;$\,\,a=1,..,M$ .We use it to find the distribution of derivatives of these eigenphases over the energy ("phaseshift times") as well as over an arbitrary external parameter.We also find the parametric correlations of Wigner-Smith delay times