Origin of hyperdiffusion in generalized Brownian motion

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 $T_{\mathrm{kin}}(t)\propto t^{\lambda }$ from the thermal bath temperature $T$ to some maximal kinetic temperature $T_{\max }$. This hyperdiffusive transient regime ceases when the particles arrive at the maximal kinetic temperature.

Phys. Rev. Lett., in press

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• Anomalous Diffusion of Inertial, Weakly Damped Particles
• Universal fluctuations in subdiffusive transport
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