Critical Slowing Down in Stochastic Processes. II : Noise-Induced Long-Time Tail in Random Growing-Rate Models
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概要
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Exact solutions of the random growing-rate models dx/dt=(γ+η(t))x-gx^m for Gaussian white noise η(t) are obtained for an arbitrary value of m(> 1) to give the noise-induced long-time tail <x^p(t)> ≇ t^<1/2> for large t at the critical point for any positive value of p. This confirms the phenomenological arguments in the first paper of this series. That is, this noise-induced long-time tail appears due to the balance (or cancellation) between the nonlinear term and noise term. Another intuitive explanation of this noise-induced long-time tail is presented on the basis of the asymptotic behavior of the normalization factor for the distribution function. A slowing down of < x^p(t)> for p < 0 at a`transition point'γ=γ(p)=∣p∣ε is also discussed.
- 理論物理学刊行会の論文
- 1982-07-25
著者
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Takesue Shinji
Department Of Physics Kyoto University
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Sasagawa Fumiyoshi
Department Of Physics Faculty Of Science Chiba University:department Of Physics Faculty Of Science T
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Suzuki Masuo
Department Of Applied Physics Science University Of Tokyo
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TAKESUE Shinji
Department of Physics, Tokyo University
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Suzuki Masuo
Physics Department, Saitama University
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