Open AccessFluctuating phase rigidity for a quantum chaotic system with partially broken time-reversal symmetry
Author(s) -
S. A. van Langen,
Piet W. Brouwer,
C. W. J. Beenakker
Publication year - 1997
Publication title -
physical review. e, statistical physics, plasmas, fluids, and related interdisciplinary topics
Language(s) - English
Resource type - Journals
eISSN - 1095-3787
pISSN - 1063-651X
DOI - 10.1103/physreve.55.r1
Subject(s) - physics , rigidity (electromagnetism) , hamiltonian (control theory) , eigenvalues and eigenvectors , quantum mechanics , unitary state , symmetry breaking , mathematical physics , gaussian , t symmetry , quantum , mathematics , mathematical optimization , political science , law , superconductivity
The functional defined as the squared modulus of the spatial average of thewave function squared, plays the role of an ``order parameter'' for thetransition between Hamiltonian ensembles with orthogonal and unitary symmetry.Upon breaking time-reversal symmetry, the order parameter crosses over from oneto zero. We compute its distribution in the crossover regime and find that ithas large fluctuations around the ensemble average. These fluctuations implylong-range spatial correlations in the eigenfunction and non-Gaussianperturbations of eigenvalues, in precise agreement with results by Fal'ko andEfetov and by Taniguchi, Hashimoto, Simons, and Altshuler. As a thirdimplication of the order-parameter fluctuations we find correlations in theresponse of an eigenvalue to independent perturbations of the system.Comment: 4 pages, REVTeX-3.0, 1 figure. Reference added to Y. V. Fyodorov and A. D. Mirlin, Phys. Rev. B 51, 13403 (1995
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