Asymptotic Property of Probability Distribution in the Relaxation from an Unstable Point : Path Integral Approach

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概要

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• A path integral formulation is developed to investigate the asymptotic property of the distribution function in the relaxation from an unstable point to stable points. The small Gaussian white noise is assumed in the stochastic process. A WKB-like asymptotic evaluation in a time-reversed motion, which is useful in discussing the enhancement of the fluctuation into a macroscopic size, is proposed. The scaling property of the distribution function can be obtained in a restricted region. For small noise strength ε, the asymptotic from of the distribution function P(x, t)=C exp(J_0(x, t)/ε+J_1(x, t)+・・・) is justifies by the WKB-like approximation. The asymptotic form breaks down for large times. Near the breaking time, another distribution having the above asymptotic from bifurcates and then approaches the final equilibrium distribution.

• 理論物理学刊行会の論文
• 1982-03-25

著者

• Otsuka Jinya

  Department Of Applied Biological Science Science University Of Tokyo

• KUNISAWA Takashi

  Department of Applied Biological Science Science University of Tokyo

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