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首页> 外文期刊>Physica, A. Statistical mechanics and its applications >Non-Markovian effects on the Brownian motion of a free particle
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Non-Markovian effects on the Brownian motion of a free particle

机译：非马尔可夫效应对自由粒子布朗运动的影响

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摘要

Non-Markovian effects on the Brownian movement of a free particle in the presence as well as in the absence of inertial force are investigated under the framework of generalized FokkerPlanck equations (Rayleigh and Smoluchowski equations). More specifically, it is predicted that non-Markovian features can diminish the values of both the root mean square displacement and the root mean square momentum, thereby assuring the mathematical property of analyticity of such physically observable quantities for all times t<0. Accordingly, the physical concept of non-Markovian Brownian trajectory turns out to be mathematically well defined by differentiable functions for all t<0. Another consequence of the non-Markovicity property is that the Langevin stochastic equations underlying the FokkerPlanck equations should be interpreted as genuine differential equations and not as integral equations according to a determined interpretation rule (Doob's rule, for instance).
机译：在广义FokkerPlanck方程（Rayleigh和Smoluchowski方程）的框架下，研究了存在和不存在惯性力对自由粒子布朗运动的非马尔可夫效应。更具体地，可以预测，非马尔可夫特征可以减小均方根位移和均方根动量的值，从而确保在所有时间t ＜0下这种物理可观察量的解析性的数学性质。因此，对于所有t ＜0，非马尔可夫布朗轨迹的物理概念在数学上被可微分函数很好地定义。非Markovicity属性的另一个结果是，根据确定的解释规则（例如，Doob规则），应将FokkerPlanck方程基础的Langevin随机方程解释为真正的微分方程，而不应解释为积分方程。

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