Dynamics of Rotating Bose--Einstein Condensates and its Efficient and Accurate Numerical Computation
Authors:
- Weizhu BaoWBWeizhu Bao
- Qiang DuQDQiang Du
- Yanzhi ZhangYZYanzhi Zhang
- 1 January 2006
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Applied Mathematics
- Vol. 66 (3) , 758-786
Abstract
In this paper, we study the dynamics of rotating Bose--Einstein condensates (BEC) based on the Gross--Pitaevskii equation (GPE) with an angular momentum rotation term and present an efficient and accurate algorithm for numerical simulations. We examine the conservation of the angular momentum expectation and the condensate width and analyze the dynamics of a stationary state with a shift in its center. By formulating the equation in either the two-dimensional polar coordinate system or the three-dimensional cylindrical coordinate system, the angular momentum rotation term becomes a term with constant coefficients. This allows us to develop an efficient time-splitting method which is time reversible, unconditionally stable, efficient, and accurate for the problem. Moreover, it conserves the position density. We also apply the numerical method to study issues such as the stability of central vortex states and the quantized vortex lattice dynamics in rotating BEC.Keywords
This publication has 47 references indexed in Scilit:
- Computing the Ground State Solution of Bose--Einstein Condensates by a Normalized Gradient FlowSIAM Journal on Scientific Computing, 2004
- Three-dimensional simulation of jet formation in collapsing condensatesJournal of Physics B: Atomic, Molecular and Optical Physics, 2003
- Dissipative Flow and Vortex Shedding in the Painlevé Boundary Layer of a Bose-Einstein CondensatePhysical Review Letters, 2003
- Numerical solution of the Gross–Pitaevskii equation for Bose–Einstein condensationJournal of Computational Physics, 2003
- Numerical Study of Time-Splitting Spectral Discretizations of Nonlinear Schrödinger Equations in the Semiclassical RegimesSIAM Journal on Scientific Computing, 2003
- An Explicit Unconditionally Stable Numerical Method for Solving Damped Nonlinear Schrödinger Equations with a Focusing NonlinearitySIAM Journal on Numerical Analysis, 2003
- Multiscale Stochastic Volatility AsymptoticsMultiscale Modeling & Simulation, 2003
- On Time-Splitting Spectral Approximations for the Schrödinger Equation in the Semiclassical RegimeJournal of Computational Physics, 2002
- Vortices in a rotating Bose-Einstein condensate: Critical angular velocities and energy diagrams in the Thomas-Fermi regimePhysical Review A, 2001
- Observation of Bose-Einstein Condensation in a Dilute Atomic VaporScience, 1995