Exploring level statistics from quantum chaos to localization with the autocorrelation function of spectral determinants

The autocorrelation function of spectral determinants (ASD) is used to characterize the discrete spectrum of a phase coherent quasi-one-dimensional, disordered metal wire as a function of its length L at 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.