RANDOM-MATRIX THEORIES IN QUANTUM PHYSICS - COMMON CONCEPTS

We review the development of random-matrix theory (RMT) during the las t fifteen years. We emphasize both the theoretical aspects, and the ap plication of the theory to a number of fields. These comprise chaotic and disordered systems, the localization problem, many-body quantum sy stems, the Calogero-Sutherland model, chiral symmetry breaking in QCD, and quantum gravity in two dimensions. The review is preceded by a bri ef historical survey of the developments of RMT and of localization th eory since their inception. We emphasize the concepts common to the ab ove-mentioned fields as well as the great diversity of RMT. In view of the universality of RMT, we suggest that the current development sign als the emergence of a new ''statistical mechanics'': Stochasticity an d general symmetry requirements lead to universal laws not based on dy namical principles. (C) 1998 Elsevier Science B.V. All rights reserved .