Non-ergodicity and fluctuations in mesoscopic insulators: The replica cooperon and diffuson

We explore the mesoscopic conductance fluctuations in the insulating regime within the Nguyen, Spivak, and Shklovskii model. We find that fluctuations of the log-conductance are persistent above the decorrelation field B_c in the insulating regime. Using the replica approach, we derive the field coupling and fluctuations in terms of "cooperon" and "diffuson" analogs and determine new corrections to temperature dependencies for small ΔB. We also analyze the ergodicity of fluctuations in the log-conductance and its scaling properties, and discuss the asymptotic validity of the usual criterion involving the commutability of disorder and field fluctuation averages.