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arXiv · 0909.0881

Foundation of Fractional Langevin Equation: Harmonization of a Many Body Problem

Ludvig Lizana·Tobias Ambjornsson·Alessandro Taloni·Eli Barkai·Michael A. Lomholt
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Abstract

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 new 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.

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Ludvig Lizana, Tobias Ambjornsson, Alessandro Taloni, Eli Barkai, Michael A. Lomholt. 2009-09-04. Foundation of Fractional Langevin Equation: Harmonization of a Many Body Problem. https://doi.org/10.1103/physreve.81.051118

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