Colloquium: Random matrices and chaos in nuclear spectra

Journal Article · Sun Jul 15 00:00:00 EDT 2007 · Reviews of Modern Physics

DOI:https://doi.org/10.1103/REVMODPHYS.79.997· OSTI ID:21013710

Papenbrock, T; Weidenmueller, H A ^[1]

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1. Department of Physics and Astronomy, University of Tennessee, Knoxville, Tennessee 37996 (United States) and Physics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831 (United States)

Chaos occurs in quantum systems if the statistical properties of the eigenvalue spectrum coincide with predictions of random-matrix theory. Chaos is a typical feature of atomic nuclei and other self-bound Fermi systems. How can the existence of chaos be reconciled with the known dynamical features of spherical nuclei? Such nuclei are described by the shell model (a mean-field theory) plus a residual interaction. The question is answered using a statistical approach (the two-body random ensemble): The matrix elements of the residual interaction are taken to be random variables. Chaos is shown to be a generic feature of the ensemble and some of its properties are displayed, emphasizing those which differ from standard random-matrix theory. In particular, the existence of correlations among spectra carrying different quantum numbers is demonstrated. These are subject to experimental verification.

• OSTI ID: 21013710
• Journal Information: Reviews of Modern Physics, Vol. 79, Issue 3; Other Information: DOI: 10.1103/RevModPhys.79.997; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 0034-6861
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGEBRA
CHAOS THEORY
CORRELATIONS
EIGENFUNCTIONS
EIGENVALUES
ENERGY LEVELS
FERMIONS
MASS NUMBER
MATRICES
MATRIX ELEMENTS
MEAN-FIELD THEORY
QUANTUM NUMBERS
RANDOMNESS
RESIDUAL INTERACTIONS
SHELL MODELS
SPIN
STATISTICAL MODELS
TWO-BODY PROBLEM
VERIFICATION