Semiclassical approach to parametric spectral correlation with spin 1/2

Taro Nagao, Keiji Saitou

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

The spectral correlation of a chaotic system with spin 1/2 is universally described by the GSE (Gaussian symplectic ensemble) of random matrices in the semiclassical limit. In semiclassical theory, the spectral form factor is expressed in terms of the periodic orbits and the spin state is simulated by the uniform distribution on a sphere. In this paper, instead of the uniform distribution, we introduce Brownian motion on a sphere to yield the parametric motion of the energy levels. As a result, the small time expansion of the form factor is obtained and found to be in agreement with the prediction of parametric random matrices in the transition within the GSE universality class. Moreover, by starting the Brownian motion from a point distribution on the sphere, we gradually increase the effect of the spin and calculate the form factor describing the transition from the Gaussian orthogonal ensemble class to the GSE class.

Original languageEnglish
Article number004
Pages (from-to)12055-12070
Number of pages16
JournalJournal of Physics A: Mathematical and Theoretical
Volume40
Issue number40
DOIs
Publication statusPublished - 2007 Oct 5
Externally publishedYes

Fingerprint

spectral correlation
form factors
Ensemble
Form Factors
Brownian movement
Random Matrices
Uniform distribution
Brownian motion
Chaotic systems
Electron energy levels
Semiclassical Limit
Orbits
energy levels
Energy Levels
Chaotic System
Periodic Orbits
Universality
orbits
expansion
predictions

ASJC Scopus subject areas

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics
  • Modelling and Simulation
  • Statistics and Probability

Cite this

Semiclassical approach to parametric spectral correlation with spin 1/2. / Nagao, Taro; Saitou, Keiji.

In: Journal of Physics A: Mathematical and Theoretical, Vol. 40, No. 40, 004, 05.10.2007, p. 12055-12070.

Research output: Contribution to journalArticle

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