The mutual influence of two layers with strongly loclized electrons is exercised through the random Coulomb shifts of site energies in one layer caused by electron hops in the other layer. We trace how these shifts give rise to a voltage drop in the passive layer, when a current is passed through the active layer. We find that the microscopic origin of drag lies in the time correlations of the occupation numbers of the sites involved in a hop. These correlations are neglected within the conventional Miller-Abrahams scheme for calculating the hopping resistance.
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