Foundation of fractional Langevin equation: harmonization of a many-body problem.
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.
Lizana
Ludvig
L
Niels Bohr Institute, Blegdamsvej 17, DK-2100 Copenhagen, Denmark.
Ambjörnsson
Tobias
T
Taloni
Alessandro
A
Barkai
Eli
E
Lomholt
Michael A
MA