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Effects of strong electric fields on hopping conductivity are studiedtheoretically. Monte-Carlo computer simulations show that the analytical theoryof Nguyen and Shklovskii [Solid State Commun. 38, 99 (1981)] provides anaccurate description of hopping transport in the limit of very high electricfields and low concentrations of charge carriers as compared to theconcentration of localization sites and also at the relative concentration ofcarriers equal to 0.5. At intermediate concentrations of carriers between 0.1and 0.5 computer simulations evidence essential deviations from the results ofthe existing analytical theories.  The theory of Nguyen and Shklovskii also predicts a negative differentialhopping conductivity at high electric fields. Our numerical calculationsconfirm this prediction qualitatively. However the field dependence of thedrift velocity of charge carriers obtained numerically differs essentially fromthe one predicted so far. Analytical theory is further developed so that itsagreement with numerical results is essentially improved.

Hopping conduction in strong electric fields: Negative differential conductivity