Universal Fluctuations and Coherence Lengths in Chaotic Mesoscopic Systems and Nuclei

TL;DR

This paper explores universal fluctuations in mesoscopic systems and nuclei using Random Matrix Theory, analyzing the density of maxima in observables like conductance and cross sections, with implications for quantum dots and nuclear astrophysics.

Contribution

It introduces an analytical approach to study universal fluctuations in mesoscopic systems and nuclei, linking statistical properties to physical observables across different contexts.

Findings

Average density of maxima in conductance fluctuations analyzed

Density of maxima in nuclear cross sections linked to astrophysical conditions

Use of the Stub model for analytical results in quantum systems

Abstract

We discuss the phenomenon of universal fluctuations in mesoscopic systems and nuclei. For this purpose we use Random Matrix Theory (RMT). The statistical $S$-matrix is used to obtain the physical observables in the case of Quantum Dots, both the Schr\"odinger and the Dirac types. To obtain analytical results, we use the Stub model. In all cases we concentrate our attention on the average density of maxima in the fluctuating observables, such as the electronic conductance. The case of neutron capture by a variety of nuclei at thermal energies is also considered. Here the average density of maxima in the cross section vs. the mass number is analysed and traced to astrophysical conditions.