Nonlinear Schrödinger Equations for Bose-Einstein Condensates

Luigi Galati; Shijun Zheng

doi:10.1063/1.4828682

Nonlinear Schrödinger Equations for Bose-Einstein Condensates

Luigi Galati, Shijun Zheng

Mathematical Sciences

Georgia Southern University

Research output: Contribution to book or proceeding › Chapter

14 Scopus citations

Abstract

The Gross-Pitaevskii equation, or more generally the nonlinear Schrödinger equation, models the Bose-Einstein condensates in a macroscopic gaseous superfluid wave-matter state in ultra-cold temperature. We provide analytical study of the NLS with L² initial data in order to understand propagation of the defocusing and focusing waves for the BEC mechanism in the presence of electromagnetic fields. Numerical simulations are performed for the two-dimensional GPE with anisotropic quadratic potentials.

Original language	American English
Title of host publication	Nonlinear and Modern Mathematical Physics: AIP Conference Proceedings
DOIs	https://doi.org/10.1063/1.4828682
State	Published - Oct 1 2013

Keywords

BEC
Electromagnetic potential
Gross-Pitaevskii equation
Nonlinear Schroedinger equation

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Mathematics

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title = "Nonlinear Schr{\"o}dinger Equations for Bose-Einstein Condensates",

abstract = "The Gross-Pitaevskii equation, or more generally the nonlinear Schr{\"o}dinger equation, models the Bose-Einstein condensates in a macroscopic gaseous superfluid wave-matter state in ultra-cold temperature. We provide analytical study of the NLS with L2 initial data in order to understand propagation of the defocusing and focusing waves for the BEC mechanism in the presence of electromagnetic fields. Numerical simulations are performed for the two-dimensional GPE with anisotropic quadratic potentials.",

keywords = "BEC, Electromagnetic potential, Gross-Pitaevskii equation, Nonlinear Schroedinger equation",

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T1 - Nonlinear Schrödinger Equations for Bose-Einstein Condensates

AU - Galati, Luigi

AU - Zheng, Shijun

PY - 2013/10/1

Y1 - 2013/10/1

N2 - The Gross-Pitaevskii equation, or more generally the nonlinear Schrödinger equation, models the Bose-Einstein condensates in a macroscopic gaseous superfluid wave-matter state in ultra-cold temperature. We provide analytical study of the NLS with L2 initial data in order to understand propagation of the defocusing and focusing waves for the BEC mechanism in the presence of electromagnetic fields. Numerical simulations are performed for the two-dimensional GPE with anisotropic quadratic potentials.

AB - The Gross-Pitaevskii equation, or more generally the nonlinear Schrödinger equation, models the Bose-Einstein condensates in a macroscopic gaseous superfluid wave-matter state in ultra-cold temperature. We provide analytical study of the NLS with L2 initial data in order to understand propagation of the defocusing and focusing waves for the BEC mechanism in the presence of electromagnetic fields. Numerical simulations are performed for the two-dimensional GPE with anisotropic quadratic potentials.

KW - BEC

KW - Electromagnetic potential

KW - Gross-Pitaevskii equation

KW - Nonlinear Schroedinger equation

UR - https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/254

UR - https://doi.org/10.1063/1.4828682

U2 - 10.1063/1.4828682

DO - 10.1063/1.4828682

M3 - Chapter

BT - Nonlinear and Modern Mathematical Physics: AIP Conference Proceedings

ER -

Nonlinear Schrödinger Equations for Bose-Einstein Condensates

Abstract

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