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Herleitung kinetischer gleichungen mit dem verallgemeinerten Stratonovich-Verfahren

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  • Gerlich, G.
  • Kagermann, H.

Abstract

The kinetic equations for the 2-time conditional probability density are derived for Coulomb systems and coupled one-dimensional harmonic oscillators. The coupled oscillators are also treated exactly. The exact second central moment of the space coordinate is compared with that derived from the kinetic equation. This shows which approximations of the generalized Stratonovich method can be responsible for the possibly irreversible character of the derived kinetic equations. Using the approximation of long difference times the kinetic equations for Coulumb systems with and without homogeneous external magnetic field are transformed into the well-known Balescu-Lenard equations.

Suggested Citation

  • Gerlich, G. & Kagermann, H., 1977. "Herleitung kinetischer gleichungen mit dem verallgemeinerten Stratonovich-Verfahren," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 88(2), pages 283-304.
    • Handle: RePEc:eee:phsmap:v:88:y:1977:i:2:p:283-304
    DOI: 10.1016/0378-4371(77)90005-X
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    Cited by:

    1. Gerlich, G. & Kagermann, H., 1982. "Über kinetische gleichungen für stochastische Prozesse mit entstehenden und vergehenden Pfaden," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 115(1), pages 247-258.
    2. 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.
    3. Kagermann, H., 1982. "Stochastic equations arising from test particle problems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 116(1), pages 199-206.

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