Stochastic resonance in bistable systems with nonlinear dissipation and multiplicative noise: A microscopic approach

Details Stochastic resonance in bistable systems with nonlinear dissipation and multiplicative noise: A microscopic approach Stochastic resonance in bistable systems with nonlinear dissipation and multiplicative noise: A microscopic approach

2012-03-04

arxiv.org/abs/1203.0770v4

Physics

Condensed Matter

Statistical Mechanics

26 pages, 10 figures, augmented with added pdf figures

Scientific paper

The stochastic resonance (SR) in bistable systems has been extensively discussed with the use of {\it phenomenological} Langevin models. By using the {\it microscopic}, generalized Caldeira-Leggett (CL) model, we study in this paper, SR of an open bistable system coupled to a bath with a nonlinear system-bath interaction. The adopted CL model yields the non-Markovian Langevin equation with nonlinear dissipation and state-dependent diffusion which preserve the fluctuation-dissipation relation (FDR). From numerical calculations, we find the following: (1) the spectral power amplification (SPA) exhibits SR not only for $a$ and $b$ but also for $\tau$ while the stationary probability distribution function is independent of them where $a$ ($b$) denotes the magnitude of multiplicative (additive) noise and $\tau$ expresses the relaxation time of colored noise; (2) the SPA for coexisting additive and multiplicative noises has a single-peak but two-peak structure as functions of $a$, $b$ and/or $\tau$. These results (1) and (2) are qualitatively different from previous ones obtained by phenomenological Langevin models where the FDR is indefinite or not held.

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