Relaxation at Critical Points: Deterministic and Stochastic Theory.
CENTER FOR NAVAL ANALYSES ARLINGTON VA
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A generalized critical point is characterized by totally non-linear dynamics. The deterministic and stochastic theory of relaxation is formulated at such a point. Canonical problems are used to motivate the general solutions. In the deterministic theory, at the critical point certain modes have polynomial rather than exponential growth or decay. The stochastic relaxation rates can be calculated in terms of various incomplete special functions. Three examples are considered. First, a substrate inhibited reaction marginal type dynamical system. Second, the relaxation of a mean field ferromagnet. A result is obtained that generalizes the work of Griffiths et al. Third, the relaxation of a critical harmonic oscillator, is considered.
- Statistics and Probability