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

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.

References in corpus (4)

• Scattering, reflection and impedance of waves in chaotic and disordered systems with absorption
• Universal Quantum Graphs
• Induced Time-Reversal Symmetry Breaking Observed in Microwave Billiards
• Spectral statistics in an open parametric billiard system

Cited by in corpus (8)

• Nodal portraits of quantum billiards: Domains, lines, and statistics
• Green's function approach for quantum graphs: an overview
• Conductance Peak Density in Nanowires
• Correlation functions and correlation widths in Quantum-Chaotic Scattering for mesoscopic systems and nuclei
• Fluctuations in the ${}^{235}$U(n,f) cross section
• Closed and open superconducting microwave waveguide networks as a model for quantum graphs
• Time-Reversal Symmetry Breaking and Decoherence in Chaotic Dirac Billiards
• Entanglement Distribution Statistic in Andreev Billiards