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Theory of the relaxation and fluctuation from unstable and metastable states

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  • Shimizu, T.

Abstract

An extension of the usual system-size expansion method is given to study the relaxation and fluctuation from unstable and metastable states. The short-time and the long-time behavior of the moments y(t) and Mn(t) and of the distribution function P(x, t) of a macroscopic variable x are investigated by using the generating function G(α, β; t) = δ(α − y(t))Π∞n = 2δ(βn − Mn(t)), where y(t) = ∫ xP(x, t) dx and Mn(t) ≡ ∫ (x − y(t))nP(x, t) dx. The dominant part of the time evolution of G(α, β; t) is extracted by introducing a scale transformation of β. The theory is applied to the one-dimensional laser model.

Suggested Citation

  • Shimizu, T., 1978. "Theory of the relaxation and fluctuation from unstable and metastable states," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 91(3), pages 534-548.
    • Handle: RePEc:eee:phsmap:v:91:y:1978:i:3:p:534-548
    DOI: 10.1016/0378-4371(78)90196-6
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    References listed on IDEAS

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    1. Tomita, Kazuhisa & Todani, Takao & Kidachi, Hideyuki, 1976. "Irreversible circulation and the undamped spiking in lasers," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 84(2), pages 350-370.
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