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