Diffusion in infinite and semi-infinite lattices with long-range coupling

Details Diffusion in infinite and semi-infinite lattices with long-range coupling Diffusion in infinite and semi-infinite lattices with long-range coupling

2011-12-30

arxiv.org/abs/1201.0133v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

4 pages, 5 figures, submitted for publication

Scientific paper

We prove that for a one-dimensional infinite lattice, with long-range coupling among sites, the diffusion of an initial delta-like pulse in the bulk, is ballistic at all times. We obtain a closed-form expression for the mean square displacement (MSD) as a function of time, and show some cases including finite range coupling, exponentially decreasing coupling and power-law decreasing coupling. For the case of an initial excitation at the edge of the lattice, we find an approximate expression for the MSD that predicts ballistic behavior at long times, in agreement with numerical results.

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