American Institute of Mathematical Sciences

Advanced
March  2010, 3(1): 181-194. doi: 10.3934/krm.2010.3.181

Numerical simulation of trapped dipolar quantum gases: Collapse studies and vortex dynamics

Zhongyi Huang 1, , Peter A. Markowich 2, and  Christof Sparber 2,

1. 

Dept. of Mathematical Sciences, Tsinghua University, Beijing 100084
2. 

Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom

Received  November 2009 Revised  December 2009 Published  January 2010

We numerically study the three dimensional Gross-Pitaevskii equation for dipolar quantum gases using a time-splitting algorithm. We are mainly concerned with numerical investigations of the possible blow-up of solutions, i.e. collapse of the condensate, and the dynamics of vortices.
Keywords: Bose-Einstein condensates, time-splitting spectral method., dipolar interactions.
Mathematics Subject Classification: Primary: 81Q99, 65M99; Secondary: 65Z0.
Citation: Zhongyi Huang, Peter A. Markowich, Christof Sparber. Numerical simulation of trapped dipolar quantum gases: Collapse studies and vortex dynamics. Kinetic and Related Models, 2010, 3 (1) : 181-194. doi: 10.3934/krm.2010.3.181
[1]

Yongming Luo, Athanasios Stylianou. On 3d dipolar Bose-Einstein condensates involving quantum fluctuations and three-body interactions. Discrete and Continuous Dynamical Systems - B, 2021, 26 (6) : 3455-3477. doi: 10.3934/dcdsb.2020239
[2]

Weizhu Bao, Loïc Le Treust, Florian Méhats. Dimension reduction for dipolar Bose-Einstein condensates in the strong interaction regime. Kinetic and Related Models, 2017, 10 (3) : 553-571. doi: 10.3934/krm.2017022
[3]

Vladimir S. Gerdjikov. Bose-Einstein condensates and spectral properties of multicomponent nonlinear Schrödinger equations. Discrete and Continuous Dynamical Systems - S, 2011, 4 (5) : 1181-1197. doi: 10.3934/dcdss.2011.4.1181
[4]

Florian Méhats, Christof Sparber. Dimension reduction for rotating Bose-Einstein condensates with anisotropic confinement. Discrete and Continuous Dynamical Systems, 2016, 36 (9) : 5097-5118. doi: 10.3934/dcds.2016021
[5]

P.G. Kevrekidis, Dimitri J. Frantzeskakis. Multiple dark solitons in Bose-Einstein condensates at finite temperatures. Discrete and Continuous Dynamical Systems - S, 2011, 4 (5) : 1199-1212. doi: 10.3934/dcdss.2011.4.1199
[6]

Pedro J. Torres, R. Carretero-González, S. Middelkamp, P. Schmelcher, Dimitri J. Frantzeskakis, P.G. Kevrekidis. Vortex interaction dynamics in trapped Bose-Einstein condensates. Communications on Pure and Applied Analysis, 2011, 10 (6) : 1589-1615. doi: 10.3934/cpaa.2011.10.1589
[7]

Vadym Vekslerchik, Víctor M. Pérez-García. Exact solution of the two-mode model of multicomponent Bose-Einstein condensates. Discrete and Continuous Dynamical Systems - B, 2003, 3 (2) : 179-192. doi: 10.3934/dcdsb.2003.3.179
[8]

Dong Deng, Ruikuan Liu. Bifurcation solutions of Gross-Pitaevskii equations for spin-1 Bose-Einstein condensates. Discrete and Continuous Dynamical Systems - B, 2019, 24 (7) : 3175-3193. doi: 10.3934/dcdsb.2018306
[9]

Liren Lin, I-Liang Chern. A kinetic energy reduction technique and characterizations of the ground states of spin-1 Bose-Einstein condensates. Discrete and Continuous Dynamical Systems - B, 2014, 19 (4) : 1119-1128. doi: 10.3934/dcdsb.2014.19.1119
[10]

Kui Li, Zhitao Zhang. A perturbation result for system of Schrödinger equations of Bose-Einstein condensates in $\mathbb{R}^3$. Discrete and Continuous Dynamical Systems, 2016, 36 (2) : 851-860. doi: 10.3934/dcds.2016.36.851
[11]

Xuguang Lu. Long time strong convergence to Bose-Einstein distribution for low temperature. Kinetic and Related Models, 2018, 11 (4) : 715-734. doi: 10.3934/krm.2018029
[12]

Brahim Alouini. Long-time behavior of a Bose-Einstein equation in a two-dimensional thin domain. Communications on Pure and Applied Analysis, 2011, 10 (6) : 1629-1643. doi: 10.3934/cpaa.2011.10.1629
[13]

Anne de Bouard, Reika Fukuizumi, Romain Poncet. Vortex solutions in Bose-Einstein condensation under a trapping potential varying randomly in time. Discrete and Continuous Dynamical Systems - B, 2015, 20 (9) : 2793-2817. doi: 10.3934/dcdsb.2015.20.2793
[14]

Weizhu Bao, Yongyong Cai. Mathematical theory and numerical methods for Bose-Einstein condensation. Kinetic and Related Models, 2013, 6 (1) : 1-135. doi: 10.3934/krm.2013.6.1
[15]

Brahim Alouini, Olivier Goubet. Regularity of the attractor for a Bose-Einstein equation in a two dimensional unbounded domain. Discrete and Continuous Dynamical Systems - B, 2014, 19 (3) : 651-677. doi: 10.3934/dcdsb.2014.19.651
[16]

Brahim Alouini. Finite dimensional global attractor for a Bose-Einstein equation in a two dimensional unbounded domain. Communications on Pure and Applied Analysis, 2015, 14 (5) : 1781-1801. doi: 10.3934/cpaa.2015.14.1781
[17]

Zhong Tan, Huaqiao Wang, Yucong Wang. Time-splitting methods to solve the Hall-MHD systems with Lévy noises. Kinetic and Related Models, 2019, 12 (1) : 243-267. doi: 10.3934/krm.2019011
[18]

José A. Carrillo, Katharina Hopf, Marie-Therese Wolfram. Numerical study of Bose–Einstein condensation in the Kaniadakis–Quarati model for bosons. Kinetic and Related Models, 2020, 13 (3) : 507-529. doi: 10.3934/krm.2020017
[19]

Chaoxu Pei, Mark Sussman, M. Yousuff Hussaini. A space-time discontinuous Galerkin spectral element method for the Stefan problem. Discrete and Continuous Dynamical Systems - B, 2018, 23 (9) : 3595-3622. doi: 10.3934/dcdsb.2017216
[20]

Gengen Zhang. Time splitting combined with exponential wave integrator Fourier pseudospectral method for quantum Zakharov system. Discrete and Continuous Dynamical Systems - B, 2022, 27 (5) : 2587-2606. doi: 10.3934/dcdsb.2021149

2020 Impact Factor: 1.432

Tools

Metrics

  • PDF downloads (93)
  • HTML views (0)
  • Cited by (3)

Other articles
by authors

[Back to Top]

Copyright © 2022 American Institute of Mathematical Sciences | Privacy Policy