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An Isaac Newton Institute Workshop

Recent Perspectives in Random Matrix Theory and Number Theory

Compund nucleus resonances, random matrices, quantum chaos

1st April 2004

Author: Oriol Bohigas (LPTMS Orsay)

Abstract

Wigner introduced random matrices in physics when searching for a guiding principle to understand properties of the compound nucleus resonances. At the end the experimental observations turned out to be remarkably consistent with random matrix theory predictions. Could random matrix theory be justified in dynamical terms? To answer this question deep connections between quantum bahaviour of classically chaotic systems (quantum chaos) and random matrices have been established. Open problems still remain. Some highlights of this long excursion, covering more than fourty years, will be given.