Invariant random matrix ensembles as models for ergodic and nonergodic hamiltonian systems

Standard random matrix ensembles, for example the well-known Gaussian ensembles, have been generally developed as models for ergodic Hamiltonian systems. Herein we consider invariant matrix ensembles that model the energy level statistics of nonergodic systems, and contain the ergodic limit as a spe...

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Bibliographic Details
Published inJournal of molecular structure Vol. 292; pp. 197 - 205
Main Authors Leitner, David M., Cederbaum, L.S.
Format Journal Article Conference Proceeding
LanguageEnglish
Published Amsterdam Elsevier B.V 01.03.1993
Elsevier
Subjects
Exact sciences and technology
Logic, set theory, and algebra
Mathematical methods in physics
Physics
Invariant
Ergodicity
Hamiltonian system
Models
Random matrix
Statistics
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Summary:Standard random matrix ensembles, for example the well-known Gaussian ensembles, have been generally developed as models for ergodic Hamiltonian systems. Herein we consider invariant matrix ensembles that model the energy level statistics of nonergodic systems, and contain the ergodic limit as a special case. We compare the ensemble presented here to the matrix element distribution of a model Hamiltonian that has been block-diagonalized to an ‘ensemble’ of small blocks.
ISSN:0022-2860
1872-8014
DOI:10.1016/0022-2860(93)80100-A