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Spectral statistics of scale invariant systems

  • T. H. Seligman
  • J. J. M. Verbaarschot
II. Spectra and States
Part of the Lecture Notes in Physics book series (LNP, volume 263)

Abstract

We give both numerical and analytical results for the spectral statistics of two dimensional systems with a homegeneous polynomial as potential. When the hamiltonian is time reversal invariant we find a gradual transition from the Poisson ensemble to the GOE going from the classically integrable to the classically chaotic case. When the time reversal symmetry is broken we find the statistics of the GUE. Most features observed in the numerical calculations, with inclusion of the ‘kink’ in the Δ3 statistic for integrable integrable systems and the asymptotic logarithmic behaviour for chaotic systems, are described by the semiclassical limit of the fluctuating part of the level density. It is shown that the transition to the chaotic regime can be described in the semiclassical limit. Finally, we construct a random matrix model that describes well the short range behaviour of all statistics studied.

Keywords

Lyapunov Exponent Random Matrix Semiclassical Limit Spectral Statistic Time Reversal Symmetry 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1986

Authors and Affiliations

  • T. H. Seligman
    • 1
  • J. J. M. Verbaarschot
    • 2
  1. 1.Instituto de FisicaUniversity of Mexico in Cuernavaca (UNAM)Mexico DFMexico
  2. 2.Department of PhysicsUniversity of Illinois at Urbana-Champaign Loomis LaboratoryUrbana

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