Werner Ebeling, Udo Erdmann, Lutz Schimansky-Geier, Frank Schweitzer:

Complex Motion of Brownian Particles with Energy Supply
Stochastic and Chaotic Dynamics in the Lakes
(Eds. D. S. Broomhead, E. A. Luchinskaya, P. V. E. McClintock, T. Mullin),
American Institute of Physics, Melville, NY, USA, 2000, pp. 183-190

We study a model of Brownian particles which are pumped with energy by means of a non-linear friction function. Analytical solutions of the corresponding Fokker-Planck equation are presented and compared with computer simulations. Different to the case of passive Brownian motion, we find several new features of the dynamics, such as the formation of limit cycles, a large mean squared displacement which increases quadratically with the energy supply, or non-equilibrium velocity distributions with crater-like form. In the four-dimensional phase space, the corresponding distribution has the form of two hoops or two tires. Further, the general features of motion in arbitrary two-dimensional potentials are discussed within a diffusion approximation.



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