Nonlinear Krönig-Penney model

Details Nonlinear Krönig-Penney model Nonlinear Krönig-Penney model

2004-06-29

arxiv.org/abs/cond-mat/0406702v2

Physics

Condensed Matter

Other Condensed Matter

4 pages, 4 figures. Phys. Rev. E. 70, (2004) (in press)

Scientific paper

We study the nonlinear Schr\"odinger equation with a periodic delta-function potential. This realizes a nonlinear Kr\"onig-Penney model, with physical applications in the context of trapped Bose-Einstein condensate alkaly gases and in the transmission of signals in optical fibers. We find analytical solutions of zero-current Bloch states. Such wave-functions have the same periodicity of the potential, and, in the linear limit, reduce to the Bloch functions of the Kr\"onig-Penney model. We also find new classes of solutions having a periodicity different from that of the external potential. We calculate the chemical potential of such states and compare it with the linear excitation spectrum.

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