Relaxation functions of the Ornstein-Uhlenbeck process with fluctuating diffusivity
Relaxation functions of the Ornstein-Uhlenbeck process with fluctuating diffusivity
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具有波动扩散率的 Ornstein-Uhlenbeck 过程的弛豫函数
DOI：
10.1103/physreve.99.032127
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发表时间：
2019
影响因子：
2.4
通讯作者：
Takashi Uneyama; Tomoshige Miyaguchi; Takuma Akimoto
中科院分区：
文献类型：
--
作者：
松枝宏明;Takashi Uneyama; Tomoshige Miyaguchi; Takuma Akimoto
研究了扩散系数随时间变化的Ornstein-Uhlenbeck(OU)过程的松弛行为。在这个过程中，位置矢量的动力学由线性恢复力和波动扩散系数(FD)的朗之万方程来描述。这一过程可以被解释为具有内部自由度或在不同环境中的松弛动力学的简单模型。利用泛函积分表达式和传递矩阵方法，我们证明了对于一般的FD过程，松弛函数可以用传递矩阵的特征值和特征函数来表示。我们将我们的一般理论应用于两个简单的FD过程，其中FD由马尔可夫两态模型或OU型过程描述。我们给出了这些模型中松弛函数的解析表达式及其渐近形式。我们还证明了具有FD的OU过程的驰豫行为与由广义朗之万方程等传统模型得到的结果有本质的不同。
We study the relaxation behavior of the Ornstein-Uhlenbeck (OU) process with time-dependent and fluctuating diffusivity. In this process, the dynamics of the position vector is modeled by the Langevin equation with a linear restoring force and a fluctuating diffusivity (FD). This process can be interpreted as a simple model of relaxational dynamics with internal degrees of freedom or in a heterogeneous environment. By utilizing the functional integral expression and the transfer matrix method, we show that the relaxation function can be expressed in terms of the eigenvalues and eigenfunctions of the transfer matrix for general FD processes. We apply our general theory to two simple FD processes where the FD is described by the Markovian two-state model or an OU-type process. We show analytic expressions of the relaxation functions in these models and their asymptotic forms. We also show that the relaxation behavior of the OU process with an FD is qualitatively different from those obtained from conventional models such as the generalized Langevin equation.