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We consider a charged Brownian gas under the influence of external, staticand uniform electric and magnetic fields, immersed in a uniform bathtemperature. We obtain the solution for the associated Langevin equation, andthereafter the evolution of the nonequilibrium temperature towards anonequilibrium (hot) steady state. We apply our results to a simple yetrelevant Brownian model for carrier transport in GaAs. We obtain a negativedifferential conductivity regime (Gunn effect) and discuss and compare ourresults with experimental results.

Hot Brownian Carriers in the Langevin Picture: Application to a simple model for the Gunn Effect in GaAs