Correlation Widths in Quantum--Chaotic Scattering

TL;DR

This paper demonstrates that the Weisskopf estimate accurately approximates the correlation width in quantum-chaotic scattering, even with few channels, by analyzing the scattering matrix autocorrelation function.

Contribution

The study shows that the Weisskopf estimate effectively predicts the correlation width in quantum-chaotic scattering, extending its validity to scenarios with few channels.

Findings

The Weisskopf estimate closely matches the actual correlation width Gamma_{corr}.

The estimate also applies well to the cross-section correlation function.

The approximation holds even when the number of channels is small.

Abstract

An important parameter to characterize the scattering matrix S for quantum-chaotic scattering is the width Gamma_{corr} of the S-matrix autocorrelation function. We show that the "Weisskopf estimate" d/(2pi) sum_c T_c (where d is the mean resonance spacing, T_c with 0 <= T_c <= 1 the "transmission coefficient" in channel c and where the sum runs over all channels) provides a very good approximation to Gamma_{corr} even when the number of channels is small. That same conclusion applies also to the cross-section correlation function.