1203.0770 (Hideo Hasegawa)

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

Hideo Hasegawa

The stochastic resonance (SR) in bistable systems has been extensively discussed with the use of {\it phenomenological} Langevin models. In this paper, we study SR of an open bistable system subjected to a bath coupled with a nonlinear system-bath interaction, which is described by the {\it microscopic}, generalized Caldeira-Leggett (CL) model. The adopted CL model yields the non-Markovian Langevin equation with nonlinear dissipation and state-dependent diffusion which preserve the fluctuation-dissipation relation (FDR). Our numerical calculations show that (1) the stationary probability distribution function is independent of noise parameters of $a$, $b$ and $\tau$ although the spectral power amplification (SPA) depends on them where $a$ ($b$) denotes the magnitude of multiplicative (additive) noise and $\tau$ expresses the relaxation time of colored noise, (2) the SPA exhibits SR not only for $a$ and $b$ but also for $\tau$, and (3) 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)-(3) are in contrast with previous ones obtained by the universal colored-noise approximation applied to phenomenological Langevin models where the FDR is not held.

View original: http://arxiv.org/abs/1203.0770