Origin of hyperdiffusion in generalized Brownian motion.
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 T(kin)(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.
Siegle
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Institute of Physics, University of Augsburg, Universitätsstrasse 1, D-86135 Augsburg, Germany.
Goychuk
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Hänggi
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