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PubMed2002

Relaxation properties of weakly coupled stochastic Ginzburg-Landau models under intense noise.

We investigate time relaxation properties of some correlation functions of stochastic Ginzburg-Landau models with weak coupling and under intense noise. Using a Feynman-Kac representation and a "high-temperature"-type approach, we study the low-lying spectrum of the generator of the dynamics, which determines the relaxation properties. We give the one-particle mass and energy-momentum dispersion curve, and also the two-particle bound-state mass, and show that both masses increase with the noise strength, in contrast with the behavior in the small noise regime.

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PubMed2004

Augmented moment method for stochastic ensembles with delayed couplings. I. Langevin model.

By employing a semianalytical dynamical mean-field approximation theory previously proposed by the author [H. Hasegawa, Phys. Rev. E 67, 041903 (2003)], we have developed an augmented moment method (AMM) in order to discuss dynamics of an N -unit ensemble described by Langevin equations with delays. In an AMM, original N -dimensional stochastic delay differential equations (SDDEs) are transformed to infinite-dimensional deterministic DEs for means and correlations of local as well as global variables. Infinite-order DEs arising from the non-Markovian property of SDDE, are terminated at the finite level m in the level-m AMM (AMMm), which yields (3+m)-dimensional deterministic DEs. Model calculations have been made for linear and nonlinear Langevin models. The stationary solution of AMM for the linear Langevin model with N=1 is nicely compared to the exact result. In the nonlinear Langevin ensemble, the synchronization is shown to be enhanced near the transition point between the oscillating and nonoscillating states. Results calculated by AMM6 are in good agreement with those obtained by direct simulations.

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