Non-linear Schrödinger system for the dynamics of a binary condensate: theory and 2D numerics
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Date
2016-12
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Abstract
We present a comprehensive discussion of the mathematical framework
for binary Bose-Einstein condensates and for the rigorous derivation of their effective dynamics, governed by a system of coupled non-linear Gross-Pitaevskii equations. We also develop in the 2D case a systematic numerical study of the Gross-Pitaevskii systems in a wide range of relevant regimes of population ratios and intra-species and
inter-species interactions. Our numerical method is based on a Fourier collocation scheme in space combined with a fourth order integrating factor scheme in time.
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Keywords
Bose-Einstein condensation, multi-component mixtures, one-body reduced density matrix, scaling limits, non-linear Gross-Pitaevskii system, Fourier collocation method, integrating factor method