Non-Gaussian energy level statistics for some integrable systems

Pavel M. Bleher, Freeman J. Dyson, Joel L. Lebowitz

Research output: Contribution to journalArticlepeer-review

21 Scopus citations


The number of levels with energy less than E of an integrable quantum system with two degrees of freedom is equal to λE+sE1/4, where λ is a constant and s a fluctuating quantity with a non-Gaussian distribution. The probability distribution of s decreases roughly like exp(-s4) when s is large. The number of levels between E and E+z E is equal to λz E +rE1/4 where r is another fluctuating quantity. The distribution of r tends to a Gaussian distribution as z→0 and oscillates around some limiting non-Gaussian distribution as z→.

Original languageEnglish (US)
Pages (from-to)3047-3050
Number of pages4
JournalPhysical review letters
Issue number19
StatePublished - 1993

All Science Journal Classification (ASJC) codes

  • General Physics and Astronomy


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