Velocity distributions in nonlinear systems

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Abstract
A growing array of numerical results obtained in our laboratory indicates that, in certain situations, the Maxwellian velocity distribution for a subensemble of low-mass test particles in equilibrium with a heat bath is not valid. This paper provides a theoretical framework in which the observed non-Maxwellian distributions can be understood. The basic arguments are as follows. When the mass of a test particle is small compared with the mass of the heat bath particles, and when this particle is subjected to a strong systematic force, the resulting dynamical motion of the test particle is subjected to a friction force that is nonlinear in the velocity of the test particle. The dynamics of the test-particle motion is then governed by a nonlinear Langevin equation, and the probability density of the stochastic variables must accordingly be obtained from a related nonlinear Fokker-Planck equation. The steady-state solutions of this differential equation are seen to correspond generally to non-Maxwellian velocity distributions.