乘性互相关噪声诱导的亚稳态逃逸率
Multiplicative cross-correlated noise induced escape rate from a metastable state
摘要：
我们提出了一个分析框架来研究两个外部乘性互相关噪声过程影响下的亚稳态逃逸率。本文从具有乘性噪声过程的唯象定态Langevin描述出发，研究了由两个相互关联的高斯定态δ关联噪声过程驱动的一维非平衡开放系统的激活速率过程的Kramers理论。基于相空间中的Fokker-Planck描述，我们导出了在中到大摩擦极限下亚稳态的逃逸率，研究了关联度对逃逸率的影响。通过采用数值模拟在外部互相关的加性和乘性噪声的存在下，我们检查我们的分析形式主义的有效性恒定耗散，这表明了一个令人满意的协议，这两种方法的具体选择的噪声过程。从理论推导和数值模拟结果可以看出，通过增加外部波动的相关程度，可以提高速率。
英文摘要：
We present an analytical framework to study the escape rate from a metastable state under the influence of two external multiplicative cross-correlated noise processes. Starting from a phenomenological stationary Langevin description with multiplicative noise processes, we have investigated the Kramers' theory for activated rate processes in a nonequilibrium open system (one-dimensional in nature) driven by two external cross-correlated noise processes which are Gaussian, stationary and delta correlated. Based on the Fokker-Planck description in phase space, we then derive the escape rate from a metastable state in the moderate to large friction limit to study the effect of degree of correlation on the same. By employing numerical simulation in the presence of external cross-correlated additive and multiplicative noises we check the validity of our analytical formalism for constant dissipation, which shows a satisfactory agreement between both the approaches for the specific choice of noise processes. It is evident both from analytical development and the corresponding numerical simulation that the enhancement of rate is possible by increasing the degree of correlation of the external fluctuations.
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