弱噪声极限下二维布朗运动的随机共振现象

在弱噪声极限下，应用多维Fokker-Planck方程的与时间有关问题方面的理论，推导了对称双稳势阱中二维布朗粒子的概率跃迁速率，并基于绝热近似理论研究了弱噪声极限下受小幅低频周期力驱动的二维布朗运动的随机共振现象.与以前的结果相比，所得到的信噪比与阻尼系数的大小无关.精确的数值模拟结果进一步说明了所得的信噪比的适用性. 关键词： 二维布朗运动 弱噪声极限 随机共振 信噪比

Stochastic resonance in two-dimensional Brownian motion in the weak noise limit

The theory of LΩEGF and the scaling theory on multidimensional Fokker-Planck equations with gradient potential are applied to derive the probability transition rate for Brownian motion in a symmetric two-dimensional bistable potential. Based on the rate method in adiabatic elimination, the phenomenon of stochastic resonance is studied in this system. Compared with the known results, the analytic expression for signal-to-noise ratio derived in this study is independent of the intensity of friction,i.e. not only applicable to an overdamped system, but also applicable to a lightly damped system. Numerical simulations fruther verify the significance of the analytically approximate result.