Wannier functions analysis of the nonlinear Schrödinger equation with a periodic potential

Details Wannier functions analysis of the nonlinear Schrödinger equation with a periodic potential Wannier functions analysis of the nonlinear Schrödinger equation with a periodic potential

2002-05-19

arxiv.org/abs/cond-mat/0205401v1

Physics

Condensed Matter

5 pages, 1 figure, submitted to Phys. Rev. E

Scientific paper

10.1103/PhysRevE.66.046608

In the present Letter we use the Wannier function basis to construct lattice approximations of the nonlinear Schr\"{o}dinger equation with a periodic potential. We show that the nonlinear Schr\"{o}dinger equation with a periodic potential is equivalent to a vector lattice with long-range interactions. For the case-example of the cosine potential we study the validity of the so-called tight-binding approximation i.e., the approximation when nearest neighbor interactions are dominant. The results are relevant to Bose-Einstein condensate theory as well as to other physical systems like, for example, electromagnetic wave propagation in nonlinear photonic crystals.

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