Universal fluctuations and coherence lengths in chaotic mesoscopic systems and nuclei

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 Schrödinger 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. arXiv:1805.10356v1 [cond-mat.mes-hall]

Numerical Simulation of GUE Two-Point Correlation and Cluster Functions

“…Random matrices were introduced by Wishart in multivariate statistics in the 1920s [1] and Wigner in the study of neutron resonances in the 1950s [2]. Since then random matrix theory has found further applications in nuclear physics [3][4][5][6][7][8] as well as in quantum and wave chaos [9,10], quantum chromodynamics [11], mesoscopic physics [12,13], quantum gravity [14], numerical computation [15], number theory [16][17][18] and complex systems [19].…”