Foundation of fractional Langevin equation: harmonization of a many-body problem.
Foundation of fractional Langevin equation: harmonization of a many-body problem.
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DOI：
10.1103/physreve.81.051118
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发表时间：
2009-09
期刊：
影响因子：
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通讯作者：
L. Lizana;T. Ambjörnsson;A. Taloni;E. Barkai;M. A. Lomholt
中科院分区：
文献类型：
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作者：
L. Lizana;T. Ambjörnsson;A. Taloni;E. Barkai;M. A. Lomholt
在本研究中，我们从第一性原理推导出单粒子运动方程，从具有一般两体相互作用势的一维多粒子系统中示踪粒子的微观描述开始。利用调和技术，我们证明了得到的动力学方程属于分数阶朗之万方程，这是一种随机框架，在大量的工作中被提出作为描述异常动力学的手段。我们的工作揭示了这些现象学模型的基本假设和由科尔曼导出的关系。
In this study we derive a single-particle equation of motion, from first principles, starting out with a microscopic description of a tracer particle in a one-dimensional many-particle system with a general two-body interaction potential. Using a harmonization technique, we show that the resulting dynamical equation belongs to the class of fractional Langevin equations, a stochastic framework which has been proposed in a large body of works as a means of describing anomalous dynamics. Our work sheds light on the fundamental assumptions of these phenomenological models and a relation derived by Kollmann.