Distribution of matrix elements of chaotic systems

Mario Feingold, Asher Peres

Research output: Contribution to journalArticlepeer-review

198 Scopus citations

Abstract

When a quantum system has a chaotic classical analog, its matrix elements in the energy representation are closely related to various microcanonical averages of the classical system. The diagonal matrix elements cluster around the classical expectation values, with fluctuations similar to the values of the off-diagonal matrix elements. The latter in turn are related to the classical autocorrelations. These results imply that quantum perturbation theory must fail, for chaotic systems, in the semiclassical limit Latin small letter h with stroke0: Two arbitrarily close Hamiltonians have, in general, completely different sets of eigenvectors.

Original languageEnglish
Pages (from-to)591-595
Number of pages5
JournalPhysical Review A
Volume34
Issue number1
DOIs
StatePublished - 1 Jan 1986
Externally publishedYes

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics

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