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

DOI10.1007/978-3-319-58904-6_15zbMath1374.81104arXiv1709.04841OpenAlexW2741766356MaRDI QIDQ4593659

Alessandro Olgiati

Publication date: 22 November 2017

Published in: Advances in Quantum Mechanics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1709.04841

zbMATH Keywords

Bose-Einstein condensatemagnetic Laplacianreduced density matrixmagnetic vector potentialeffective evolution equationsmany-body quantum dynamicsmagnetic Sobolev spaceGross-Pitaevskii scalingmagnetic Gross-Pitaevskii equationnon-linear cubic Schrödinger equation

Mathematics Subject Classification ID

NLS equations (nonlinear Schrödinger equations) (35Q55) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Many-body theory; quantum Hall effect (81V70) Commutation relations and statistics as related to quantum mechanics (general) (81S05) Dynamic and nonequilibrium phase transitions (general) in statistical mechanics (82C26)

Related Items (3)

Global, finite energy, weak solutions for the NLS with rough, time-dependent magnetic potentials ⋮ Gross-Pitaevskii non-linear dynamics for pseudo-spinor condensates ⋮ Effective non-linear spinor dynamics in a spin-1 Bose–Einstein condensate

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