Non-Gaussian energy level statistics for some integrable systems

Pavel M. Bleher, Freeman J. Dyson, and Joel L. Lebowitz
Phys. Rev. Lett. 71, 3047 – Published 8 November 1993
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Abstract

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+zE is equal to λzE +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→∞.

  • Received 30 August 1993

DOI:https://doi.org/10.1103/PhysRevLett.71.3047

©1993 American Physical Society

Authors & Affiliations

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

  • School of Natural Science, Institute for Advanced Study, Princeton, New Jersey 08540
  • Departments of Mathematics and Physics, Rutgers University, New Brunswick, New Jersey 08903

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Vol. 71, Iss. 19 — 8 November 1993

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