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Motion of a particle in a velocity-dependent random force

Published online by Cambridge University Press:  14 July 2016

Karmeshu
Karmeshu*
Affiliation:
University of Delhi
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Abstract

The motion of a particle is investigated in the presence of a velocity-dependent random force assumed to be proportional to velocity. Two different possibilities are considered, namely, the presence and absence of random driving force. In the absence of random driving force, the velocity and displacement auto-correlation function are calculated. The probability distribution in velocity space is also evaluated. It is found that in the absence of intrinsic damping, the energy of the particle increases without limit. The condition for the energetic stability of the particle in the presence of random driving force is obtained. The Fokker-Planck equation for the probability distribution in velocity space is derived from the stochastic Liouville equation for delta-correlated velocity-dependent random force.

Keywords

EXACT SOLUTIONSLANGEVIN EQUATIONSTOCHASTIC DAMPINGSTOCHASTIC DRIVING FORCEDELTA-CORRELATEDSTATIONARY GAUSSIAN PROCESSENERGETIC STABILITYFOKKER-PLANCK EQUATION
Type
Research Papers
Information
Journal of Applied Probability , Volume 13 , Issue 4 , December 1976 , pp. 684 - 695
Copyright
Copyright © Applied Probability Trust 1976 

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