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Brownian motion as a problem of eliminating fast variables

Author

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  • Van Kampen, N.G.
  • Oppenheim, I.

Abstract

The Hamilton equations for a Brownian particle involve its mass as a large parameter. As a consequence its motion is relatively slow and the fast motion of the surrounding fluid molecules can be eliminated by the standard method of eliminating fast variables. The result is equivalent to the known Langevin equation, plus additional higher orders. All coefficients are expressed in terms of correlation functions of the microscopic force on the particle.

Suggested Citation

  • Van Kampen, N.G. & Oppenheim, I., 1986. "Brownian motion as a problem of eliminating fast variables," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 138(1), pages 231-248.
    • Handle: RePEc:eee:phsmap:v:138:y:1986:i:1:p:231-248
    DOI: 10.1016/0378-4371(86)90183-4
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    References listed on IDEAS

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    1. Oppenheim, Felix E., 1971. "Comment: Defense of Noncognitivism Defended," American Political Science Review, Cambridge University Press, vol. 65(4), pages 1115-1116, December.
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    Cited by:

    1. Morgado, W.A.M., 2015. "Exact cumulant Kramers–Moyal-like expansion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 438(C), pages 493-508.
    2. Schwartz, M. & Navot, Y., 1997. "Stochastic dynamics of constrained systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 245(3), pages 517-522.
    3. Janssen, J.A.M., 1988. "Solution of Kramers' problem," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 152(1), pages 145-176.
    4. Morgado, W.A.M. & Oppenheim, I., 1997. "Kinetic equations for smooth granular systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 246(3), pages 547-562.

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