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Brownian motion and quasi-Markov processes

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  • Marshall, T.W.

Abstract

We study the underdamped Brownian motion of a particle in a force field, with a stochastic force whose memory is short compared with the relaxation time, by the method of the stochastic Liouville equation. We show that such a system may be modelled approximately by a diffusion Markov process, if the coordinates used to describe it are the action variables of the unperturbed motion. The resulting Fokker-Planck equation is closely related to certain evolution equations obtained in Old Quantum Theory.

Suggested Citation

  • Marshall, T.W., 1980. "Brownian motion and quasi-Markov processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 103(1), pages 172-182.
    • Handle: RePEc:eee:phsmap:v:103:y:1980:i:1:p:172-182
    DOI: 10.1016/0378-4371(80)90212-5
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    References listed on IDEAS

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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. Florence Dinerstein, 1977. "To Terry and her husband who killed her," Review of Radical Political Economics, Union for Radical Political Economics, vol. 9(3), pages 22-23, October.
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