Adaptive continuation algorithms for computing energy levels of rotating Bose-Einstein condensates

DOI10.1016/j.cpc.2007.06.009zbMath1196.82107OpenAlexW2122311744MaRDI QIDQ710136

Shing-Lin Chang, Cheng-Sheng Chien

Publication date: 18 October 2010

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

Full work available at URL: https://doi.org/10.1016/j.cpc.2007.06.009

zbMATH Keywords

finite difference methodbifurcationnonlinear Schrödinger equationangular momentumadaptive continuation method

Mathematics Subject Classification ID

Related Items

Efficient and accurate gradient flow methods for computing ground states of spinor Bose-Einstein condensates, An adaptive multigrid scheme for Bose-Einstein condensates in a periodic potential, 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, Computing multiple peak solutions for Bose-Einstein condensates in optical lattices, Exploring bistability in rotating Bose-Einstein condensates by a quotient transformation invariant continuation method, A spectral collocation method for a rotating Bose-Einstein condensation in optical lattices, A spectral-Galerkin continuation method using Chebyshev polynomials for the numerical solutions of the Gross-Pitaevskii equation, Spectral collocation methods using sine functions for a rotating Bose-Einstein condensation in optical lattices, Exploring ground states and excited states of spin-1 Bose-Einstein condensates by continuation methods, Stability analysis and continuation for the coupled Gross-Pitaevskii equations, Superconvergence of high-order FEMs for eigenvalue problems with periodic boundary conditions, A two-parameter continuation algorithm for vortex pinning in rotating Bose-Einstein condensates, Numerical modeling of exciton-polariton Bose-Einstein condensate in a microcavity, Two-stage continuation algorithms for Bloch waves of Bose-Einstein condensates in optical lattices, A spectral-Galerkin continuation method for numerical solutions of the Gross-Pitaevskii equation, A finite difference continuation method for computing energy levels of Bose-Einstein condensates, Superconvergence of bi-\(k\)-Lagrange elements for eigenvalue problems, Multi-parameter continuation and collocation methods for rotating multi-component Bose–Einstein condensates, A constrained gentlest ascent dynamics and its applications to finding excited states of Bose-Einstein condensates

Uses Software

• Matlab

Cites Work

• Multiple interior peak solutions for some singularly perturbed Neumann problems.
• Numerical solution of the Gross--Pitaevskii equation for Bose--Einstein condensation
• Multiple boundary peak solutions for some singularly perturbed Neumann problems
• Ground, symmetric and central vortex states in rotating Bose-Einstein condensates
• Structure-Preserving Methods for Computing Eigenpairs of Large Sparse Skew-Hamiltonian/Hamiltonian Pencils
• Optimizing Schrödinger Functionals Using Sobolev Gradients: Applications to Quantum Mechanics and Nonlinear Optics
• Structure of a quantized vortex in boson systems
• NUMERICAL CONTINUATION FOR NONLINEAR SCHRÖDINGER EQUATIONS
• PLTMGC: A Multigrid Continuation Program for Parameterized Nonlinear Elliptic Systems
• Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems
• Spectral Methods in MATLAB