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Remarks on the Derivation of Gross-Pitaevskii Equation with Magnetic Laplacian

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Advances in Quantum Mechanics

Part of the book series: Springer INdAM Series ((SINDAMS,volume 18))

Abstract

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.

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Acknowledgements

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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Authors and Affiliations

  1. SISSA - International School for Advanced Studies, via Bonomea 265, Trieste, Italy

    Alessandro Olgiati

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  1. Alessandro Olgiati
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Correspondence to Alessandro Olgiati .

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Editors and Affiliations

  1. International Sch. for Advanced Studies, SISSA, Trieste, Italy

    Alessandro Michelangeli

  2. International Sch. for Advanced Studies, SISSA and Sapienza University of Rome, Trieste, Italy

    Gianfausto Dell'Antonio

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Olgiati, A. (2017). Remarks on the Derivation of Gross-Pitaevskii Equation with Magnetic Laplacian. In: Michelangeli, A., Dell'Antonio, G. (eds) Advances in Quantum Mechanics. Springer INdAM Series, vol 18. Springer, Cham. https://doi.org/10.1007/978-3-319-58904-6_15

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