On mathematical models for Bose-Einstein condensates in optical lattices (expanded version)
arXiv:0810.4003 · doi:10.1142/S0129055X0900361X
Abstract
Our aim is to analyze the various energy functionals appearing in the physics literature and describing the behavior of a Bose-Einstein condensate in an optical lattice. We want to justify the use of some reduced models. For that purpose, we will use the semi-classical analysis developed for linear problems related to the Schrödinger operator with periodic potential or multiple wells potentials. We justify, in some asymptotic regimes, the reduction to low dimensional problems and analyze the reduced problems.
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Cited by in corpus (4)
- Unstable normalized standing waves for the space periodic NLS
- The Fokker-Planck equation for bosons in 2D: well-possedness and asymptotic analysis
- Counting function of magnetic resonances for exterior problems
- Vortex families near a spectral edge in the Gross-Pitaevskii equation with a two-dimensional periodic potential