Introduction to Matrix Models

Abstract

Nuclear levels. In 1951 E. Wigner [1] proposed, as a first approach to the understanding of the structure of the eigenstates of complex nuclei, to sustitute to the Schrödinger equation, in which the forces between the nucleons are not very well-known, and whose solution requires drastic simplifying assumptions, a simple random Hamiltonian drawn from a Gaussian ensemble. The only constraints are imposed by symmetries, such as time-reversal symmetry, and the need to focus on a sequence of levels with given angular momentum and parity. This approach was then developped considerably by Dyson [2, 3], Mehta [4] and hundreds of followers. Numerous review articles on nuclear data show that the level spacing distribution, as drawn from random matrix theory, fits well the measured level spacing on a large sequence of nuclei, see, for instance, [4].

Unité Mixte de Recherche 8549 du Centre National de la Recherche Scientifique et de l’’cole Normale Supérieure.