Level broadening and quantum interference effects in insulators

We study quantum interference effects in the context of the Nguyen-Spivak-Shklovskii (NSS) model including level broadening due to inelastic events. Improving on a recent mean-field approach, we incorporate path correlations and study both the log-conductance and its fluctuations. In contrast with mean field, we find that all changes in the conductance, due to broadening, imply corrections to the localization length. Furthermore, the change in the magnetoconductance sign, predicted by mean field, is not borne out by direct solution of the NSS model within reasonable broadening parameters. We compute a phase diagram for the magnetoconductance in the broadening parameter space and propose a replica theory for weak inelastic events.