Abstract
The non-linear Gross-Pitaevskii (GP) equation plays an important role in the mean-field theory of the Bose-Einstein condensation and has interesting mathematical properties. In this lecture we consider two nontrivial problems related to physical interpretation of the solutions of the GP equation: the superfluidity of a BEC gas in an optical lattice and the superfluidity of a 1D Bose-gas, with special attention to the role of grey solitons.
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Pitaevskii, L. (2004). Bose-Einstein Condensation: The Odd Nonlinear Quantum Mechanics. In: Abdullaev, F.K., Konotop, V.V. (eds) Nonlinear Waves: Classical and Quantum Aspects. NATO Science Series II: Mathematics, Physics and Chemistry, vol 153. Springer, Dordrecht. https://doi.org/10.1007/1-4020-2190-9_16
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DOI: https://doi.org/10.1007/1-4020-2190-9_16
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