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Level statistics of a pseudo-Hermitian Dicke model

Tetsuo Deguchi1,*, Pijush K. Ghosh2,†, and Kazue Kudo3,‡

  • 1Department of Physics, Graduate School of Humanities and Sciences, Ochanomizu University, 2-1-1 Ohtsuka, Bunkyo-ku, Tokyo 112-8610, Japan
  • 2Department of Physics, Siksha-Bhavana, Visva-Bharati University, Santiniketan PIN 731 235, India
  • 3Ochadai Academic Production, Division of Advanced Sciences, Ochanomizu University, 2-1-1 Ohtsuka, Bunkyo-ku, Tokyo 112-8610, Japan

  • *deguchi@phys.ocha.ac.jp
  • †pijushkanti.ghosh@visva-bharati.ac.in
  • ‡kudo.kazue@ocha.ac.jp
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Phys. Rev. E 80, 026213 – Published 20 August, 2009

DOI: https://doi.org/10.1103/PhysRevE.80.026213

Abstract

A non-Hermitian operator that is related to its adjoint through a similarity transformation is defined as a pseudo-Hermitian operator. We study the level statistics of a pseudo-Hermitian Dicke Hamiltonian that undergoes quantum phase transition (QPT). We find that the level-spacing distribution of this Hamiltonian near the integrable limit is close to Poisson distribution, while it is Wigner distribution for the ranges of the parameters for which the Hamiltonian is nonintegrable. We show that the assertion in the context of the standard Dicke model that QPT is a precursor to a change in the level statistics is not valid in general.

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Phys. Rev. E 80, 026213– Published 20 August, 2009
  • Received 15 April 2009

© 2009 American Physical Society

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