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We study quantum interference effects on the transition strength for stronglylocalized electrons hopping on 2D square and 3D cubic lattices in a magneticfield B. In 2D, we obtain closed-form expressions for the tunneling probabilitybetween two arbitrary sites by exactly summing the corresponding phase factorsof all directed paths connecting them. An analytic expression for themagnetoconductance, as an explicit function of the magnetic flux, is derived.In the experimentally important 3D case, we show how the interference patternsand the small-B behavior of the magnetoconductance vary according to theorientation of B.Comment: 4 pages, RevTe

Strongly Localized Electrons in a Magnetic Field: Exact Results on Quantum Interference and Magnetoconductance