Random Matrix Thermodynamics

摘要

We have performed a study of the statistical mechanics of correlated spectra first introduced by Dyson and Mehta some 40 years ago. We have derived a modified thermodynamical statistics (a number and its variance) for linear spectra. This approach was used to analyze the statistical properties of the eigenvalues of random matrices of Gaussian ensembles and of the experimental eigenfrequencies of acoustic resonances of an aluminum plate cut in the shape of a chaotic billiard. The results obtained suggest that this statistics provides a robust tool for the investigation of spectral properties.