Remarks on the Derivation of Gross-Pitaevskii Equation with Magnetic Laplacian
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The effective dynamics for a Bose-Einstein condensate in the regime of high dilution and subject to an external magnetic field is governed by a magnetic Gross-Pitaevskii equation. We elucidate the steps needed to adapt to the magnetic case the proof of the derivation of the Gross-Pitaevskii equation within the “projection counting” scheme.
KeywordsBose-Einstein condensate Effective evolution equations Gross-Pitaevskii scaling Magnetic Gross-Pitaevskii equation Magnetic Laplacian Magnetic Sobolev space Magnetic vector potential Many-body quantum dynamics Non-linear cubic Schrödinger equation Reduced density matrix
Alessandro Olgiati is Partially supported by the 2014–2017 MIUR-FIR grant “Cond-Math: Condensed Matter and Mathematical Physics”, code RBFR13WAET and by Gruppo Nazionale per la Fisica Matematica (GNFM-INdAM). The author also warmly thanks the GSSI, for the kind hospitality and financial support during a visit in L’Aquila.
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