Bounds on the tight-binding approximation for the Gross-Pitaevskii equation with a periodic potential

Details Bounds on the tight-binding approximation for the Gross-Pitaevskii equation with a periodic potential Bounds on the tight-binding approximation for the Gross-Pitaevskii equation with a periodic potential

2007-11-16

arxiv.org/abs/0711.2694v1

Physics

Mathematical Physics

9 pages, 2 figures

Scientific paper

We justify the validity of the discrete nonlinear Schrodinger equation for the tight-binding approximation in the context of the Gross-Pitaevskii equation with a periodic potential. Our construction of the periodic potential and the associated Wannier functions is based on the previous work, while our analysis involving energy estimates and Gronwall's inequality addresses time-dependent localized solutions on large but finite time intervals.

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