R Klages and N Korabel 2002 J. Phys. A: Math. Gen. 35 4823 doi:10.1088/0305-4470/35/23/302
Understanding deterministic diffusion by correlated random walks
R Klages and N Korabel
Show affiliationsLow-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.
- PACS
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05.40.Fb Random walks and Levy flights
- MSC
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37D45 Strange attractors, chaotic dynamics
82C41 Dynamics of random walks, random surfaces, lattice animals, etc. (See also 60G50)
- Subjects
- Dates
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Issue 23 (14 June 2002)
Received 21 February 2002
Published 31 May 2002
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Understanding deterministic diffusion by correlated random walks
R Klages and N Korabel 2002 J. Phys. A: Math. Gen. 35 4823
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