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Employing the Monte Carlo technique hopping at the Fermi level in a cubic lattice has been simulated as a function of temperature, electric field, hopping parameter 2α, and time. It has been found that the predictions of the simple theories agree remarkably well with our computer experiments. In our work we find a true d.c. conductivity proportional to exp -(T0/T)1/4 at low temperatures. The time dependence shows dispersion at short times due to energy relaxation and later equilibrium to the average hopping distance

MONTE CARLO SIMULATION OF VARIABLE RANGE HOPPING AT THE FERMI LEVEL