Origin of hyperdiffusion in generalized Brownian motion

TL;DR

This paper investigates the origin of hyperdiffusion in a non-Markovian generalized Langevin equation model, revealing a transient superdiffusive regime linked to particle heating before reaching ballistic motion.

Contribution

It introduces a minimal non-Markovian model that explains hyperdiffusion as a transient phenomenon due to velocity correlations and particle heating in generalized Brownian motion.

Findings

Identification of transient hyperdiffusion with $< ext{Δ}x^2(t)> ext{∝} t^{2+ ext{λ}}$

Link between hyperdiffusion and transient kinetic temperature increase

Hyperdiffusive regime ends at maximal kinetic temperature

Abstract

We study a minimal non-Markovian model of superdiffusion which originates from long-range velocity correlations within the generalized Langevin equation (GLE) approach. The model allows for a three-dimensional Markovian embedding. The emergence of a transient hyperdiffusion, $< \Delta x^2(t)> \propto t^{2+\lambda}$, with $\lambda\sim 1-3$ is detected in tilted washboard potentials before it ends up in a ballistic asymptotic regime. We relate this phenomenon to a transient heating of particles $T_{\rm kin}(t)\propto t^\lambda$ from the thermal bath temperature $T$ to some maximal kinetic temperature $T_{\rm max}$. This hyperdiffusive transient regime ceases when the particles arrive at the maximal kinetic temperature.