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Relaxation mode analysis of nonlinear birth and death processes

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Abstract

Nonlinear birth and death processes with one variable are considered. The general master equations describing these processes are analyzed in terms of their eigenmodes and eigenvalues using the method of a WKB approximation. Formulas for the density of eigenstates are obtained. The lower lying eigenmodes are calculated to investigate long-time relaxation, such as relaxations of metastable and unstable states. Anomalous accumulation of the lower lying eigenvalues is shown to exist when the system is infinitesimally close to a critical or marginal state. The general results obtained are applied to some instructive examples, such as the kinetic Weiss-Ising model and a stochastic model of nonlinear chemical reactions.

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Authors and Affiliations

  1. Department of Physics, University of Tokyo, Bunkyo-ku, Tokyo, Japan

    Kazuhiro Matsuo

  2. Department of Chemistry, University of California, San Diego, La Jolla, California

    Kazuhiro Matsuo

Authors
  1. Kazuhiro Matsuo
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Additional information

The work at UCSD was supported in part by the National Science Foundation under Grants MPS72-04363A03 and CHE75-20624.

Adapted from the author's Ph.D. dissertation at University of Tokyo, December 1974.

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Matsuo, K. Relaxation mode analysis of nonlinear birth and death processes. J Stat Phys 16, 169–195 (1977). https://doi.org/10.1007/BF01418750

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  • DOI: https://doi.org/10.1007/BF01418750

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