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Revisit to the scaling theory of transient phenomena — Generalization to correlated noise and singular perturbation expansion up to infinite order

Author

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  • Suzuki, Masuo
  • Liu, Yong
  • Tsuno, Takashi

Abstract

A scaling theory is formulated in nonlinear Langevin equations with colored noise near the instability point from which the center of the initial distribution is deviated slightly. An intuitive derivation is given as well as perturbational calculations up to the infinite order of the noise. Moments of all orders are calculated in the approximation in which only the most dominant terms are retained in the scaling limit. Hence the scaling distribution function is also obtained. The onset time t0 is derived as a functional of the correlation function of the noise and it is shown to increase when the noise correlation length increases.

Suggested Citation

  • Suzuki, Masuo & Liu, Yong & Tsuno, Takashi, 1986. "Revisit to the scaling theory of transient phenomena — Generalization to correlated noise and singular perturbation expansion up to infinite order," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 138(3), pages 433-455.
    • Handle: RePEc:eee:phsmap:v:138:y:1986:i:3:p:433-455
    DOI: 10.1016/0378-4371(86)90026-9
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    References listed on IDEAS

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    1. De Pasquale, F. & Tartaglia, P. & Tombesi, P., 1979. "Transient laser radiation as a stochastic process near an instability point," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 99(3), pages 581-591.
    2. Ding, E-Jiang, 1983. "Asymptotic properties of the Markovian master equations for multi-stationary systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 119(1), pages 317-326.
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