Remarks on the derivation of Gross-Pitaevskii equation with magnetic Laplacian
Alessandro Olgiati
TL;DR
This paper discusses how to adapt the derivation of the Gross-Pitaevskii equation for Bose-Einstein condensates to include effects of an external magnetic field using a projection counting method.
Contribution
It provides a detailed adaptation of the proof for deriving the magnetic Gross-Pitaevskii equation within the projection counting framework.
Findings
Extended the derivation method to magnetic settings
Clarified the steps for incorporating magnetic Laplacian
Validated the approach for high dilution regimes
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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Taxonomy
TopicsCold Atom Physics and Bose-Einstein Condensates · Strong Light-Matter Interactions · Atomic and Subatomic Physics Research