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Understanding deterministic diffusion by correlated random walks

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Klages,  R.
Max Planck Institute for the Physics of Complex Systems, Max Planck Society;

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Korabel,  N.
Max Planck Institute for the Physics of Complex Systems, Max Planck Society;

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Citation

Klages, R., & Korabel, N. (2002). Understanding deterministic diffusion by correlated random walks. Journal of Physics A-Mathematical and General, 35(23), 4823-4836. Retrieved from http://www.iop.org/EJ/abstract/0305-4470/35/23/302.


Cite as: http://hdl.handle.net/11858/00-001M-0000-002B-375F-C
Abstract
Low-dimensional periodic arrays of scatterers with a moving point particle are ideal models for studying deterministic diffusion. For such systems the diffusion coefficient is typically an irregular function under variation of a control parameter. Here we propose a systematic scheme of how to approximate deterministic diffusion coefficients of this kind in terms of correlated random walks. We apply this approach to two simple examples which are a one-dimensional map on the line, and the periodic Lorentz gas. Starting from suitable Green-Kubo formulae we evaluate hierarchies of approximations for their parameter-dependent diffusion coefficients. These approximations converge exactly yielding a straightforward interpretation of the structure of these irregular diffusion coefficients in terms of dynamical correlations.