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Fluctuating phase rigidity for a quantum chaotic system with partially broken time-reversal symmetry

S. A. van Langen, P. W. Brouwer, and C. W. J. Beenakker
Phys. Rev. E 55, R1(R) – Published 1 January 1997

Abstract

The functional ρ=|∫dr-→ψ2|2 measures the phase rigidity of a chaotic wave function ψ(r-→) in the transition between Hamiltonian ensembles with orthogonal and unitary symmetry. Upon breaking time-reversal symmetry, ρ crosses over from one to zero. We compute the distribution of ρ in the crossover regime and find that it has large fluctuations around the ensemble average. These fluctuations imply long-range spatial correlations in ψ and non-Gaussian perturbations of eigenvalues, in precise agreement with results by Fal'ko and Efetov [Phys. Rev. Lett. 77, 912 (1996)] and by Taniguchi et al. [Europhys. Lett. 27, 335 (1994)]. As a third implication of the phase-rigidity fluctuations we find correlations in the response of an eigenvalue to independent perturbations of the system.

  • Received 10 September 1996

DOI:https://doi.org/10.1103/PhysRevE.55.R1

©1997 American Physical Society

Authors & Affiliations

S. A. van Langen, P. W. Brouwer, and C. W. J. Beenakker

  • Instituut-Lorentz, University of Leiden, P.O. Box 9506, 2300 RA Leiden, The Netherlands

Issue

Vol. 55, Iss. 1 — January 1997

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