2000/06/30 by Nilanjana Datta, Datta, Nilanjana, Herve Kunz +2
Chemistry · Physics and Astronomy · #Condensed Matter (cond-mat) #FOS: Physical sciences #Molecular spectroscopy and chirality #Quantum Mechanics and Applications #Spectroscopy and Quantum Chemical Studies #cond-mat
paper · pdf · doi:10.48550/arxiv.cond-mat/0006488
37 pages
arxiv created 2000/06/30 · openalex publication_date 2000/06/30 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We analyze a class of parametrized Random Matrix models, introduced by\nRosenzweig and Porter, which is expected to describe the energy level\nstatistics of quantum systems whose classical dynamics varies from regular to\nchaotic as a function of a parameter. We compute the generating function for\nthe correlations of energy levels, in the limit of infinite matrix size. Our\ncomputations show that for a certain range of values of the parameter, the\nenergy-level statistics is given by that of the Wigner-Dyson ensemble. For\nanother range of parameter values, one obtains the Poisson statistics of\nuncorrelated energy levels. However, between these two ranges, new statistics\nemerge, which is neither Poissonnian nor Wigner. The crossover is measured by a\nrenormalized coupling constant. The model is exactly solved in the sense that,\nin the limit of infinite matrix size, the energy-level correlation functions\nand their generating function are given in terms of a finite set of integrals.\n