A Simple and Efficient Numerical Method for Computing the Dynamics of Rotating Bose--Einstein Condensates via Rotating Lagrangian Coordinates

Handle URI:
http://hdl.handle.net/10754/597405
Title:
A Simple and Efficient Numerical Method for Computing the Dynamics of Rotating Bose--Einstein Condensates via Rotating Lagrangian Coordinates
Authors:
Bao, Weizhu; Marahrens, Daniel; Tang, Qinglin; Zhang, Yanzhi
Abstract:
We propose a simple, efficient, and accurate numerical method for simulating the dynamics of rotating Bose-Einstein condensates (BECs) in a rotational frame with or without longrange dipole-dipole interaction (DDI). We begin with the three-dimensional (3D) Gross-Pitaevskii equation (GPE) with an angular momentum rotation term and/or long-range DDI, state the twodimensional (2D) GPE obtained from the 3D GPE via dimension reduction under anisotropic external potential, and review some dynamical laws related to the 2D and 3D GPEs. By introducing a rotating Lagrangian coordinate system, the original GPEs are reformulated to GPEs without the angular momentum rotation, which is replaced by a time-dependent potential in the new coordinate system. We then cast the conserved quantities and dynamical laws in the new rotating Lagrangian coordinates. Based on the new formulation of the GPE for rotating BECs in the rotating Lagrangian coordinates, a time-splitting spectral method is presented for computing the dynamics of rotating BECs. The new numerical method is explicit, simple to implement, unconditionally stable, and very efficient in computation. It is spectral-order accurate in space and second-order accurate in time and conserves the mass on the discrete level. We compare our method with some representative methods in the literature to demonstrate its efficiency and accuracy. In addition, the numerical method is applied to test the dynamical laws of rotating BECs such as the dynamics of condensate width, angular momentum expectation, and center of mass, and to investigate numerically the dynamics and interaction of quantized vortex lattices in rotating BECs without or with the long-range DDI.Copyright © by SIAM.
Citation:
Bao W, Marahrens D, Tang Q, Zhang Y (2013) A Simple and Efficient Numerical Method for Computing the Dynamics of Rotating Bose--Einstein Condensates via Rotating Lagrangian Coordinates. SIAM Journal on Scientific Computing 35: A2671–A2695. Available: http://dx.doi.org/10.1137/130911111.
Publisher:
Society for Industrial & Applied Mathematics (SIAM)
Journal:
SIAM Journal on Scientific Computing
KAUST Grant Number:
KUK-I1-007-43
Issue Date:
Jan-2013
DOI:
10.1137/130911111
Type:
Article
ISSN:
1064-8275; 1095-7197
Sponsors:
This research was supported by the Singapore A*STAR SERC "Complex Systems" Research Programme grant 1224504056.This author's work was supported by research award KUK-I1-007-43 from King Abdullah University of Science and Technology (KAUST).This author's work was supported by the University of Missouri Research Board, Simons Foundation award 210138, and NSF grant DMS-1217000.
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Full metadata record

DC FieldValue Language
dc.contributor.authorBao, Weizhuen
dc.contributor.authorMarahrens, Danielen
dc.contributor.authorTang, Qinglinen
dc.contributor.authorZhang, Yanzhien
dc.date.accessioned2016-02-25T12:32:33Zen
dc.date.available2016-02-25T12:32:33Zen
dc.date.issued2013-01en
dc.identifier.citationBao W, Marahrens D, Tang Q, Zhang Y (2013) A Simple and Efficient Numerical Method for Computing the Dynamics of Rotating Bose--Einstein Condensates via Rotating Lagrangian Coordinates. SIAM Journal on Scientific Computing 35: A2671–A2695. Available: http://dx.doi.org/10.1137/130911111.en
dc.identifier.issn1064-8275en
dc.identifier.issn1095-7197en
dc.identifier.doi10.1137/130911111en
dc.identifier.urihttp://hdl.handle.net/10754/597405en
dc.description.abstractWe propose a simple, efficient, and accurate numerical method for simulating the dynamics of rotating Bose-Einstein condensates (BECs) in a rotational frame with or without longrange dipole-dipole interaction (DDI). We begin with the three-dimensional (3D) Gross-Pitaevskii equation (GPE) with an angular momentum rotation term and/or long-range DDI, state the twodimensional (2D) GPE obtained from the 3D GPE via dimension reduction under anisotropic external potential, and review some dynamical laws related to the 2D and 3D GPEs. By introducing a rotating Lagrangian coordinate system, the original GPEs are reformulated to GPEs without the angular momentum rotation, which is replaced by a time-dependent potential in the new coordinate system. We then cast the conserved quantities and dynamical laws in the new rotating Lagrangian coordinates. Based on the new formulation of the GPE for rotating BECs in the rotating Lagrangian coordinates, a time-splitting spectral method is presented for computing the dynamics of rotating BECs. The new numerical method is explicit, simple to implement, unconditionally stable, and very efficient in computation. It is spectral-order accurate in space and second-order accurate in time and conserves the mass on the discrete level. We compare our method with some representative methods in the literature to demonstrate its efficiency and accuracy. In addition, the numerical method is applied to test the dynamical laws of rotating BECs such as the dynamics of condensate width, angular momentum expectation, and center of mass, and to investigate numerically the dynamics and interaction of quantized vortex lattices in rotating BECs without or with the long-range DDI.Copyright © by SIAM.en
dc.description.sponsorshipThis research was supported by the Singapore A*STAR SERC "Complex Systems" Research Programme grant 1224504056.This author's work was supported by research award KUK-I1-007-43 from King Abdullah University of Science and Technology (KAUST).This author's work was supported by the University of Missouri Research Board, Simons Foundation award 210138, and NSF grant DMS-1217000.en
dc.publisherSociety for Industrial & Applied Mathematics (SIAM)en
dc.subjectAngular momentum rotationen
dc.subjectDipole-dipole interactionen
dc.subjectGross-Pitaevskii equationen
dc.subjectRotating Bose-Einstein condensateen
dc.subjectRotating Lagrangian coordinatesen
dc.subjectTime-splittingen
dc.titleA Simple and Efficient Numerical Method for Computing the Dynamics of Rotating Bose--Einstein Condensates via Rotating Lagrangian Coordinatesen
dc.typeArticleen
dc.identifier.journalSIAM Journal on Scientific Computingen
dc.contributor.institutionNational University of Singapore, Singapore City, Singaporeen
dc.contributor.institutionMax Planck Institute for Mathematics in the Sciences, Leipzig, Germanyen
dc.contributor.institutionMissouri University of Science and Technology, Rolla, United Statesen
kaust.grant.numberKUK-I1-007-43en
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