Classical transport in quasiperiodic media

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Publication Type Journal Article
School or College College of Science
Department Mathematics
Creator Golden, Kenneth M.
Title Classical transport in quasiperiodic media
Date 1991
Description Abstract. Classical transport coefficients such as the effective conductivity or diffusivity of a quasiperiodic medium were observed [1] to depend discontinuously on the frequencies of the quasiperiodicity. For example, for a one-dimensional medium with a potential V(x) = cosx + coskx , the effective diffusion coefficient D*(k) has the same value D for all irrational k , but differs from D and depends on k for k rational, where it is thus discontinuous. Here we review some recent progress [2-4] in understanding this discontinuous behavior. In particular, a class of examples which explicitly exhibit the discontinuity in dimensions d >_ 2 is constructed. In addition, we examine some rather surprising consequences of the discontinuity for the rate of approach to limiting behavior of diffusion or conduction in quasiperiodic media as time or volume becomes infinite. It is found that these rates can be "arbitrarily slow," which contrasts with the power laws observed for random media.
Type Text
Publisher American Mathematical Society (AMS)
First Page 359
Last Page 373
Subject Transport; Diffusion; Random
Language eng
Bibliographic Citation Golden, K. M. (1991). Classical transport in quasiperiodic media. American Mathematical Society, 359-73.
Rights Management (c) American Mathematical Society
Format Medium application/pdf
Format Extent 4,210,312 bytes
Identifier ir-main,5725
ARK ark:/87278/s6fr0dzn
Setname ir_uspace
Date Created 2012-06-13
Date Modified 2012-06-13
ID 704612
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