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

@article{Martnez2012DiffusionII,
  title={Diffusion in infinite and semi-infinite lattices with long-range coupling},
  author={Alejandro J. Mart́ınez and Mario I. Molina},
  journal={Journal of Physics A},
  year={2012},
  volume={45},
  pages={275204}
}
We prove that for a one-dimensional, infinite periodic lattice, with long-range coupling among sites, the diffusion of an initial delta-like pulse in the bulk is ballistic at all times, with a ?speed? that depends on the ?smoothness? of the dispersion relation. We obtain a closed-form expression for the mean square displacement (MSD), and show some relevant examples including finite-range coupling, exponentially decreasing coupling and power-law decreasing coupling. For the case of an initial… 
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