Non-ergodic fluctuations of mesoscopic insulators with spin-orbit coupling

We present calculations of mesoscopic conductance fluctuations in the deep insulating regime (DIR) within the Nguyen, Spivak and Shklovskii with spin-orbit coupling (SOC). We show that the log-conductance is a stationarity process. A weak decaying behavior of the correlation function is found, such that Slutski's theorem can be invoked to conclude that the whole stochastic process defined by the log-conductance is non-ergodic in the mean square sense, in accordance with the behavior found for the criterion of mean square ergodicity.