Derivation of the probability distribution of velocities of a detector-recorded brownian particle

Abstract

The probability distribution of velocities in the given space region (detector) is found for particles of a passive admixture in a stream of external gas. Since direct calculation of the above probability density involves significant difficulties, the solution is based on the classical problem of the probability distribution of coordinates and velocity of a Brownian particle at a fixed time. Analyzing dependence of the solution on the parameters of the initial problem, we obtain conditions under which the assumptions on the character of particle motion hold true.