Foundation of fractional Langevin equation: Harmonization of a many-body problem

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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 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.

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  • Biophysics
Original languageEnglish
JournalPhysical Review E (Statistical, Nonlinear, and Soft Matter Physics)
Volume81
Issue number5
Publication statusPublished - 2010
Publication categoryResearch
Peer-reviewedYes