Anderson localization and the integer quantum Hall transition: a new perspective

The autocorrelation function of spectral determinants (ASD) is used to prob e a system of disordered electrons. It is represented as an effective parti tion function, and thus the problem is reduced to finding the spectrum of t he respective effective Hamiltonian. A spectral gap above its ground state is argued to be a strong indication that all states are localized. This met hod is demonstrated for electrons in a quasi-1-dimensional disordered metal wire as a function of a magnetic field, and for two-dimensional disordered electrons in weak and strong magnetic fields.