Statistical theory of energy levels and random matrices in physics

M. Carmeli

Research output: Contribution to journalReview articlepeer-review

11 Scopus citations


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.

Original languageEnglish
Pages (from-to)259-297
Number of pages39
JournalJournal of Statistical Physics
Issue number4
StatePublished - 1 Apr 1974


  • Random matrices
  • distributions
  • eigenvalues
  • energy levels
  • ensembles
  • multivariate analysis
  • nuclear physics
  • statistical theory

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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