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Statistical theory of energy levels and random matrices in physics

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Abstract

In this paper the physical aspects of the statistical theory of the energy levels of complex physical systems and their relation to the mathematical theory of random matrices are discussed. After a preliminary introduction we summarize the symmetry properties of physical systems. Different kinds of ensembles are then discussed. This includes the Gaussian, orthogonal, and unitary ensembles. The problem of eigenvalue-eigenvector distributions of the Gaussian ensemble is then discussed, followed by a discussion on the distribution of the widths. In the appendices we discuss the symplectic group and quaternions, and the Gaussian ensemble in detail.

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  1. Department of Physics, University of Negev, Beer Sheva, Israel

    M. Carmeli

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Work done while the author was at the Aerospace Research Laboratories, Wright-Patterson Air Force Base, Ohio, under Contract F33615-71-C-1463 through Technology Incorporated.

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Carmeli, M. Statistical theory of energy levels and random matrices in physics. J Stat Phys 10, 259–297 (1974). https://doi.org/10.1007/BF01012252

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