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Titolo:
SOME PROPERTIES OF INVARIANT RANDOM-MATRIX ENSEMBLES AND THEIR CONNECTION TO ERGODIC AND NONERGODIC HAMILTONIAN-SYSTEMS
Autore:
LEITNER DM; CEDERBAUM LS;
Indirizzi:
UNIV HEIDELBERG,NEUENHEIMER FELD 150 W-6900 HEIDELBERG GERMANY
Titolo Testata:
Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
fascicolo: 1, volume: 49, anno: 1994,
pagine: 114 - 121
SICI:
1063-651X(1994)49:1<114:SPOIRE>2.0.ZU;2-V
Fonte:
ISI
Lingua:
ENG
Soggetto:
ENERGY-LEVELS; FLUCTUATIONS; SPECTRUM;
Tipo documento:
Article
Natura:
Periodico
Settore Disciplinare:
Science Citation Index Expanded
Science Citation Index Expanded
Citazioni:
26
Recensione:
Indirizzi per estratti:
Citazione:
D.M. Leitner e L.S. Cederbaum, "SOME PROPERTIES OF INVARIANT RANDOM-MATRIX ENSEMBLES AND THEIR CONNECTION TO ERGODIC AND NONERGODIC HAMILTONIAN-SYSTEMS", Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 49(1), 1994, pp. 114-121

Abstract

Standard random-matrix ensembles, for example, the well-known Gaussian ensembles, are constructed under the constraint of invariance under a canonical transformation, and 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. After examining some properties of invariant matrix ensembles, we present numerical calculations of probability densities of matrix elements. We focus on theextreme case of an invariant ensemble yielding eigenvalues with Poisson statistics, i.e., level statistics of semiclassical, integrable Hamiltonians, from which we can determine essential differences between invariant ensembles modeling ergodic and nonergodic systems. The ensemble presented here is compared with aspecific model Hamiltonian, whose degree of ergodicity is determined by variation of a single parameter. The model Hamiltonian is block diagonalized to an ''ensemble'' of small blocks for parameter values varied between the ergodic and nonergodic limits. Distributions of elements observed in the blocks are compared with those predicted by the matrix ensembles.

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Documento generato il 28/09/20 alle ore 18:31:33