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

摘要

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