Cross-section Fluctuations in Open Microwave Billiards and Quantum Graphs: The Counting-of-Maxima Method Revisited

TL;DR

This paper revisits the counting-of-maxima method to analyze cross-section fluctuations in quantum-chaotic systems, using microwave billiards and quantum graphs to improve accuracy and provide analytical insights.

Contribution

It experimentally tests and refines the counting-of-maxima method for determining correlation widths in quantum-chaotic scattering, with enhanced precision and analytical descriptions.

Findings

Validated the counting-of-maxima method with high accuracy

Proposed an analytical model for resonance regions

Confirmed the constancy of the product of maxima density and correlation width

Abstract

The fluctuations exhibited by the cross-sections generated in a compound-nucleus reaction or, more generally, in a quantum-chaotic scattering process, when varying the excitation energy or another external parameter, are characterized by the width Gamma_corr of the cross-section correlation function. In 1963 Brink and Stephen [Phys. Lett. 5, 77 (1963)] proposed a method for its determination by simply counting the number of maxima featured by the cross sections as function of the parameter under consideration. They, actually, stated that the product of the average number of maxima per unit energy range and Gamma_corr is constant in the Ercison region of strongly overlapping resonances. We use the analogy between the scattering formalism for compound-nucleus reactions and for microwave resonators to test this method experimentally with unprecedented accuracy using large data sets and propose an analytical description for the regions of isolated and overlapping resonances.