A two-parameter continuation algorithm for vortex pinning in rotating Bose-Einstein condensates

DOI10.1016/j.cpc.2012.10.001zbMath1302.65232OpenAlexW2059602612MaRDI QIDQ483838

Yong-Cai Geng, Sumit K. Garg

Publication date: 17 December 2014

Published in: Computer Physics Communications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cpc.2012.10.001

zbMATH Keywords

spectral collocation methodsGross-Pitaevskii equationground state solution

Mathematics Subject Classification ID

NLS equations (nonlinear Schrödinger equations) (35Q55) PDEs in connection with quantum mechanics (35Q40) Software, source code, etc. for problems pertaining to quantum theory (81-04) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70)

Related Items (10)

A two-parameter continuation algorithm using radial basis function collocation method for rotating Bose-Einstein condensates ⋮ A two-parameter continuation method for computing numerical solutions of spin-1 Bose-Einstein condensates ⋮ Efficient continuation methods for computing ground states of quasi-2D rotating dipolar Bose-Einstein condensates ⋮ Efficient spectral computation of the stationary states of rotating Bose-Einstein condensates by preconditioned nonlinear conjugate gradient methods ⋮ Continuation and preconditioned imaginary time evolution methods for boson-fermion mixtures ⋮ BEC2HPC: a HPC spectral solver for nonlinear Schrödinger and rotating Gross-Pitaevskii equations. Stationary states computation ⋮ Stability analysis and continuation for the coupled Gross-Pitaevskii equations ⋮ C and Fortran OpenMP programs for rotating Bose-Einstein condensates ⋮ Numerical modeling of exciton-polariton Bose-Einstein condensate in a microcavity ⋮ Multi-parameter continuation and collocation methods for rotating multi-component Bose–Einstein condensates

Cites Work

• Spectral collocation methods using sine functions for a rotating Bose-Einstein condensation in optical lattices
• Convergence conditions for iterative methods seeking multi-component solitary waves with prescribed quadratic conserved quantities
• Computing multiple peak solutions for Bose-Einstein condensates in optical lattices
• Using pseudo-arclength continuation to trace the resonances of the Schrödinger equation
• A spectral-Galerkin continuation method using Chebyshev polynomials for the numerical solutions of the Gross-Pitaevskii equation
• Exploring ground states and excited states of spin-1 Bose-Einstein condensates by continuation methods
• Adaptive continuation algorithms for computing energy levels of rotating Bose-Einstein condensates
• Path following around corank-2 bifurcation points of a semi-linear elliptic problem with symmetry
• Ground, symmetric and central vortex states in rotating Bose-Einstein condensates
• A continuation BSOR-Lanczos--Galerkin method for positive bound states of a multi-component Bose-Einstein condensate
• Optimizing Schrödinger Functionals Using Sobolev Gradients: Applications to Quantum Mechanics and Nonlinear Optics
• Accelerated Imaginary‐time Evolution Methods for the Computation of Solitary Waves
• Introduction to Numerical Continuation Methods
• Numerical Methods for Bifurcations of Dynamical Equilibria
• Nonlinear modes for the Gross–Pitaevskii equation—a demonstrative computation approach

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