The Generalized Langevin Equation in Harmonic Potentials: Anomalous Diffusion and Equipartition of Energy

We consider the generalized Langevin equation (GLE) in a harmonic potential with power law decay memory. We study the anomalous diffusion of the particle’s displacement and velocity. By comparison with the free particle situation in which the velocity was previously shown to be either diffusive or subdiffusive, we find that, when trapped in a harmonic potential, the particle’s displacement may either be diffusive or superdiffusive. Under slightly stronger assumptions on the memory kernel, namely, for kernels related to the broad class of completely monotonic functions, we show that both the free particle and the harmonically bounded GLE satisfy the equipartition of energy condition. This generalizes previously known results for the GLE under particular kernel instances such as the generalized Rouse kernel or (exactly) a power law function.

• Publication year

  2021

• Venue

  Communications in Mathematical Physics

• Publication date

  2021-03-08

• Fields of study

  Mathematics, Physics

• Identifiers
  DOI 10.1007/s00220-022-04378-xarXiv 2103.05089
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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