Exploring Level Statistics from Quantum Chaos to Localization with the Autocorrelation Function of Spectral Determinants

Abstract

The autocorrelation function of spectral determinants (ASD) is used to characterize the discrete spectrum of a phase coherent quasi- 1- dimensional, disordered wire as a function of its length L in a finite, weak magnetic field. An analytical function is obtained depending only on the dimensionless conductance g= xi/L where xi is the localization length, the scaled frequency x= omega/Delta, where Delta is the average level spacing of the wire, and the global symmetry of the system. A metal- insulator crossover is observed, showing that information on localization is contained in the disorder averaged ASD.

4 pages, 3 figures

References in corpus (2)

• Secular determinants of random unitary matrices
• Characterization of Quantum Chaos by the Autocorrelation Function of Spectral Determinants

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• Magnetolocalization in disordered quantum wires
• The semiclassical origin of curvature effects in universal spectral statistics
• Symmetry Dependence of Localization in Quasi- 1- dimensional Disordered Wires