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Brownian motion of harmonic systems with fluctuating parameters

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  • West, Bruce J.
  • Lindenberg, Katja
  • Seshadri, V.

Abstract

Exact first and second order statistics of a damped mechanical oscillator with a fluctuating frequency and driven by a fluctuating force are obtained. All the cumulants of the fluctuating frequency are assumed to be delta correlated, while those of the driving force are of arbitrary form. The oscillator results depend only on the first and second order statistics of the driving force and on the coefficients of the first and second cumulants of the frequency fluctuations. Thus neither the higher order statistics of the driving force nor the coefficients of the higher cumulants of the frequency fluctuations need to be specified. When the fluctuating quantities are both delta correlated, the dynamics of the correction functions are shown to be independent of the frequency fluctuations.

Suggested Citation

  • West, Bruce J. & Lindenberg, Katja & Seshadri, V., 1980. "Brownian motion of harmonic systems with fluctuating parameters," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 102(3), pages 470-488.
    • Handle: RePEc:eee:phsmap:v:102:y:1980:i:3:p:470-488
    DOI: 10.1016/0378-4371(90)90177-T
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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.
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    1. Roerdink, J.B.T.M, 1982. "A cumulant expansion for the time correlation functions of solutions to linear stochastic differential equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 112(3), pages 557-587.
    2. Wissel, Christian, 1984. "Solution of the master equation of a bistable reaction system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 128(1), pages 150-163.
    3. Lindenberg, Katja & West, Bruce J., 1984. "Finite correlation time effects in nonequilibrium phase transitions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 128(1), pages 25-47.
    4. Schweitzer, Frank & Schimansky-Geier, Lutz & Ebeling, Werner & Ulbricht, Heinz, 1988. "A stochastic approach to nucleation in finite systems: Theory and computer simulations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 150(1), pages 261-279.
    5. Roerdink, J.B.T.M., 1981. "Inhomogeneous linear random differential equations with mutual correlations between multiplicative, additive and initial-value terms," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 109(1), pages 23-57.
    6. van Kampen, N.G., 1980. "Process with delta-correlated cumulants," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 102(3), pages 489-495.
    7. Barcons, F.X. & Garrido, L., 1983. "Systems under the influence of white and colored poisson noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 117(1), pages 212-226.

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