Title: Diffusive Behavior for Randomly Kicked Newtonian Particles in a Spatially Periodic Medium
Authors: Clark, Jeremy ×
Maes, Christian #
Issue Date: Jan-2011
Publisher: Springer-Verlag Heidelberg
Series Title: Communications in Mathematical Physics vol:301 issue:1 pages:229-283
Abstract: We prove a central limit theorem for the momentum distribution of a particle undergoing an unbiased spatially periodic random forcing at exponentially distributed times without friction. The start is a linear Boltzmann equation for the phase space density, where the average energy of the particle grows linearly in time. Rescaling time, the momentum converges to a Brownian motion, and the position is its time-integral showing superdiffusive scaling with time t(3/2). The analysis has two parts: (1) to show that the particle spends most of its time at high energy, where the spatial environment is practically invisible; (2) to treat the low energy incursions where the motion is dominated by the deterministic force, with potential drift but where symmetry arguments cancel the ballistic behavior.
ISSN: 0010-3616
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Theoretical Physics Section
× corresponding author
# (joint) last author

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