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Stochastic equations arising from test particle problems

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  • Kagermann, H.

Abstract

Dynamical functions depending on the state of one marked test particle of a classical many-body system are considered. The time evolution is described by differential equations whose coefficients are random and in addition depend on the initial state of the test-particle. To remove this dependence a weak-coupling approximation is used. Due to the finite correlation time of the driving stochastic process different equations for the test-particle propagator are obtained, if a one-time description is used. It is shown that this ambiguity is characteristic for weakly coupled systems and vanishes only in the weak-coupling limit. The generator of the resulting Markovian process consists of the differentiations with respect to the velocity- and position variables up to second order.

Suggested Citation

  • Kagermann, H., 1981. "Stochastic equations arising from test particle problems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 105(3), pages 365-379.
    • Handle: RePEc:eee:phsmap:v:105:y:1981:i:3:p:365-379
    DOI: 10.1016/0378-4371(81)90101-1
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    1. Rodríguez, R.F. & Van Kampen, N.G., 1976. "Systematic treatment of fluctuations in a nonlinear oscillator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 85(2), pages 347-362.
    2. Micheline Thomine-Desmazures, 1965. "L'investigation psychosociologique en milieu rural," Économie rurale, Programme National Persée, vol. 64(1), pages 19-24.
    3. Emmerich, Albert & Gerlich, Gerhard & Kagermann, Henning, 1978. "Particle motion in stochastic force fields," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 92(3), pages 362-378.
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