Structure of Amplitude Correlations in open chaotic Systems

TL;DR

This paper presents a simplified analytical approximation for the complex VWZ model of amplitude correlations in open quantum chaotic systems, capturing key features across parameter space with high accuracy.

Contribution

It introduces an explicit, transparent analytical form for the VWZ correlations, simplifying the complex numerical solution while maintaining accuracy.

Findings

Analytical approximation matches numerical VWZ solutions closely.

Correlation structure described by the Gorin-Seligman expression.

Correction factors highlight the role of level correlation hole.

Abstract

An analytical approximation is found for the Verbaarschot-Weidenmueller-Zirnbauer solution. Its structure is discussed. The VWZ model is believed to correctly represent the correlations of two S-matrix elements for an open quantum chaotic system, but the solution has considerable complexity and is presently only accessed numerically. The present procedure gives its features explicitly over the full range of the parameter space in a transparent and simple analytical form preserving accuracy to a considerable degree.The bulk of the VWZ correlations are described by the Gorin-Seligman expression for the 2-amplitude correlations of the Ericson-Gorin-Seligman (EGS) model. The structure of the remaining correction factors for correlation functions is discussed with special emphasis of the role of the level correlation hole both for inelastic and elastic correlations.