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

TL;DR

This paper uses the autocorrelation function of spectral determinants to analyze the transition from quantum chaos to localization in disordered wires, revealing how spectral statistics reflect localization properties.

Contribution

It introduces an analytical form of the ASD depending on conductance, frequency, and symmetry, linking spectral statistics to localization in disordered systems.

Findings

Identifies a metal-insulator crossover through ASD analysis.

Shows ASD depends on conductance and symmetry.

Demonstrates ASD captures localization information.

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.