Random Matrix Theories in Quantum Physics: Common Concepts
摘要
We review the development of random-matrix theory (RMT) during the last decade. We emphasize both the theoretical aspects, and the application of the theory to a number of fields. These comprise chaotic and disordered systems, the localization problem, many-body quantum systems, the Calogero-Sutherland model, chiral symmetry breaking in QCD, and quantum gravity in two dimensions. The review is preceded by a brief historical survey of the developments of RMT and of localization theory since their inception. We emphasize the concepts common to the above-mentioned fields as well as the great diversity of RMT. In view of the universality of RMT, we suggest that the current development signals the emergence of a new "statistical mechanics": Stochasticity and general symmetry requirements lead to universal laws not based on dynamical principles.
引用
@article{arxiv.cond-mat/9707301,
title = {Random Matrix Theories in Quantum Physics: Common Concepts},
author = {Thomas Guhr and Axel Mueller-Groeling and Hans A. Weidenmueller},
journal= {arXiv preprint arXiv:cond-mat/9707301},
year = {2016}
}
备注
178 pages, Revtex, 45 figures, submitted to Physics Reports