Memory effects, two color percolation, and the temperature dependence of Mott's variable range hopping

Abstract: There are three basic processes that determine hopping transport: (a) hopping between normally empty sites (i.e. having exponentially small occupation numbers at equilibrium); (b) hopping between normally occupied sites, and (c) transitions between normally occupied and unoccupied sites. In conventional theories all these processes are considered Markovian and the correlations of occupation numbers of different sites are believed to be small(i.e. not exponential in temperature). We show that, contrary to this belief, memory effects suppress the processes of type (c), and manifest themselves in a subleading {\em exponential} temperature dependence of the variable range hopping conductivity. This temperature dependence originates from the property that sites of type (a) and (b) form two independent resistor networks that are weakly coupled to each other by processes of type (c). This leads to a two-color percolation problem which we solve in the critical region.