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 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.

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

References in corpus (9)

• Viscoelastic subdiffusion: from anomalous to normal
• From random walk to single-file diffusion
• Fractional Langevin Equation: Over-Damped, Under-Damped and Critical Behaviors
• Single-File diffusion in a Box
• Langevin formulation for single-file diffusion
• Diffusion of Tagged Particle in an Exclusion Process
• Tagged Particle Correlations in the Asymmetric Simple Exclusion Process: Finite Size Effects
• Strong Mobility in Weakly Disordered Systems
• Scaling limits of a tagged particle in the exclusion process with variable diffusion coefficient

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