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

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

2009-09-04

arxiv.org/abs/0909.0881v2

Phys. Rev. E 81, 051118 (2010)

Physics

Condensed Matter

Statistical Mechanics

8 pages, 2 figures, REVTeX, revised with 4 appendices added, to appear in Physical Review E.

Scientific paper

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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