We study a minimal non-Markovian model of superdiffusion which originates from long-range velocity correlations within the generalized Langevin equation approach. The model allows for a three-dimensional Markovian embedding. The emergence of a transient hyperdiffusion, ⟨Δx²(t)⟩∝t^2+λ, with λ~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 Tₖᵢₙ(t)∝t^λ from the thermal bath temperature T to some maximal kinetic temperature Tmax. This hyperdiffusive transient regime ceases when the particles arrive at the maximal kinetic temperature.
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Siegle et al. (2010) studied this question.
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