Multiscale Homogenization with Bounded Ratios and Anomalous Slow Diffusion
نویسندگان
چکیده
Abstract We show that the effective diffusivity matrix D(V n) for the heat operator ∂t − (1/2 − ∇V n∇) in a periodic potential V n = n k=0 Uk(x/Rk) obtained as a superposition of Hölder-continuous periodic potentials Uk (of period Td := R d/Zd , d ∈ N∗, Uk(0) = 0) decays exponentially fast with the number of scales when the scale ratios Rk+1/Rk are bounded above and below. From this we deduce the anomalous slow behavior for a Brownian motion in a potential obtained as a superposition of an infinite number of scales, dyt = dωt − ∇V (yt )dt . c © 2002 Wiley Periodicals, Inc.
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