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Localization and spectral statistics in a banded random matrix ensemble

M Wilkinson, M Feingold and D M Leitner

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The authors investigate the localization properties of the eigenvectors of a banded random matrix ensemble, in which the diagonal matrix elements increase along the diagonal. They relate the results to a transition in the spectral statistics which is observed as a parameter is varied, and discuss the relevance of this model to the quantum mechanics of chaotic Hamiltonian systems.


PACS

05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion

05.45.Mt Quantum chaos; semiclassical methods

02.10.Ud Linear algebra

02.10.Yn Matrix theory

02.50.-r Probability theory, stochastic processes, and statistics

02.60.Dc Numerical linear algebra

MSC

15A52 Random matrices

81Q50 Quantum chaos (See also 37Dxx)

15A18 Eigenvalues, singular values, and eigenvectors

Subjects

Mathematical physics

Computational physics

Statistical physics and nonlinear systems

Dates

Issue 1 (7 January 1991)



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