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Название: Relaxation mode analysis of nonlinear birth and death processes
Автор: Matsuo K.
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.