Arbitrarily slow decay of correlations in quasiperiodic systems |
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Authors: | K Golden S Goldstein |
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Institution: | (1) Department of Mathemtics, Rutgers University, 08903 New Brunswick, New Jersey;(2) Present address: Department of Mathematics, Princeton University, 08544 Princeton, New Jersey |
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Abstract: | For diffusive motion in random media it is widely believed that the velocity autocorrelation functionc(t) exhibits power law decay as time;t![rarr](/content/x1l4n341746p3323/xxlarge8594.gif) . We demonstrate that the decay ofc(t) in quasiperiodic media can be arbitrarily slow within the class of integrable functions. For example, ind=1 with a potentialV(x)=cosx+coskx, there is a dense set of irrationalk's such that the decay ofc(k, t) is slower than 1/t
(1+ ) for any >0. The irrationals producing such a slow decay ofc(k, t) arevery well approximated by rationals. |
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Keywords: | Long-time tails quasiperiodic media velocity autocorrelation function time-dependent transport coefficients modulated structures |
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