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

TY - JOUR

T1 - Foundation of fractional Langevin equation

T2 - Harmonization of a many-body problem

AU - Lizana, George Ludvig

AU - Ambjørnsson, Tobias

AU - Taloni, A.

AU - Barkai, Eli

AU - Lomholt, M. A.

PY - 2010/5/14

Y1 - 2010/5/14

N2 - 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.

AB - 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.

U2 - 10.1103/PhysRevE.81.051118

DO - 10.1103/PhysRevE.81.051118

M3 - Journal article

SN - 2470-0045

VL - 81

SP - 051118

JO - Physical Review E

JF - Physical Review E

IS - 5

ER -