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We report the results of Monte Carlo simulation of electron dynamics instationary and space- and time-dependent electric fields in compensated GaNsamples. We have determined the frequency and wavevector dependencies of thedynamic conductivity, $\sigma_{\omega,q}$. We have found that the spatiallydependent dynamic conductivity of the drifting electrons can be negative understationary electric fields of moderate amplitudes, $2..5$ kV/cm. This effect isrealized in a set of frequency windows. The low-frequency window with negativedynamic conductivity is due to the Cherenkov mechanism. For this case thetime-dependent field induces a {\it traveling wave} of the electronconcentration in real space and a {\it standing wave} in the energy/momentumspace. The higher frequency windows of negative dynamic conductivity areassociated with the optical phonon transient time resonances. For this case thetime-dependent field is accompanied by oscillations of the electrondistribution in the form of the {\it traveling} waves in both the real spaceand the energy/momentum space. We discuss the optimal conditions for theobservation of these effects. We suggest that the studied negative dynamicconductivity can be used to amplify electromagnetic waves at the expense ofenergy of the stationary field and current.

THz frequency- and wavevector-dependent conductivity of low-density drifting electron gas in GaN. Monte Carlo calculations