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

Abstract

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.

28 pages, 10 figures, accepted in Physica A with minor changes

References in corpus (6)

• Nonlinear damping in mechanical resonators based on graphene and carbon nanotubes
• Quantum state-dependent diffusion and multiplicative noise: a microscopic approach
• A moment approach to non-Gaussian colored noises
• Classical open systems with nonlinear nonlocal dissipation and state-dependent diffusion: Dynamical responses and the Jarzynski equality
• Transient rectification of Brownian diffusion with asymmetric initial distribution
• Stationary and dynamical properties of finite $N$-unit Langevin models subjected to multiplicative noises