Random Walks through the Ensemble: Linking Spectral Statistics with Wave-Function Correlations in Disordered Metals
- 15 July 1996
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review Letters
- Vol. 77 (3) , 554-557
- https://doi.org/10.1103/physrevlett.77.554
Abstract
We use a random walk in the ensemble of impurity configurations to generate a Brownian motion model for energy levels in disordered conductors. Treating arclength along the random walk as fictitous time, the resulting Langevin equation relates spectral statistics to eigenfunction correlations. Solving this equation at energy scales large compared with the mean level spacing, we obtain the spectral form factor and its parametric dependence.Keywords
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This publication has 20 references indexed in Scilit:
- Universal correlation in the spectra of disordered systems with an Aharonov-Bohm fluxPhysical Review Letters, 1993
- The parametric number varianceNonlinearity, 1991
- Parametric motion of energy levels: Curvature distributionPhysical Review A, 1990
- Chaos in Classical and Quantum MechanicsPublished by Springer Nature ,1990
- Statistical aspects of dissipation by Landau-Zener transitionsJournal of Physics A: General Physics, 1988
- Distribution of Energy Eigenvalues in the Irregular SpectrumPhysical Review Letters, 1983
- Supersymmetry and theory of disordered metalsAdvances in Physics, 1983
- A Brownian-Motion Model for the Eigenvalues of a Random MatrixJournal of Mathematical Physics, 1962
- Statistical Theory of the Energy Levels of Complex Systems. IJournal of Mathematical Physics, 1962
- On the statistical distribution of the widths and spacings of nuclear resonance levelsMathematical Proceedings of the Cambridge Philosophical Society, 1951