Quantum ergodicity at a finite energy level

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4 Citations (Scopus)


The purpose of this paper is to formulate the notion of quantum ergodicity at a finite energy level for certain quantum mechanics, by using the method of Sunada [Sul]. Under some assumptions on the corresponding classical mechanics, we obtain a necessary and sufficient condition in terms of semi-classical asymptotic behaviour of eigenfunctions of a quantum Hamiltonian so that the classical mechanics is ergodic. We also obtain a result on quantum weak mixing at a finite energy level which is a semiclassical analogue of the notion introduced in [Z4].

Original languageEnglish
Pages (from-to)867-885
Number of pages19
JournalJournal of the Mathematical Society of Japan
Issue number4
Publication statusPublished - 1999


  • Quantum ergodicity
  • Reduction
  • Semi-classical limit

ASJC Scopus subject areas

  • Mathematics(all)


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