Ground-state solution of Bose--Einstein condensate by directly minimizing the energy functional
From MaRDI portal
Publication:1873436
DOI10.1016/S0021-9991(03)00097-4zbMath1028.82500arXivcond-mat/0303218MaRDI QIDQ1873436
Publication date: 20 May 2003
Published in: Journal of Computational Physics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/cond-mat/0303218
numerical methodfinite element approximationBose-Einstein condensationThomas-Fermi approximationGross-Pitaevskii equationEnergy functionalFinite element approximationGround-state solution
Quantum optics (81V80) Phase transitions (general) in equilibrium statistical mechanics (82B26) Computational methods for problems pertaining to quantum theory (81-08) Quantum equilibrium statistical mechanics (general) (82B10) Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60) Optimality conditions for minimax problems (49K35)
Related Items
Efficient and accurate gradient flow methods for computing ground states of spinor Bose-Einstein condensates ⋮ Numerical solution of the Gross--Pitaevskii equation for Bose--Einstein condensation ⋮ Gradient flow finite element discretizations with energy-based adaptivity for the Gross-Pitaevskii equation ⋮ A finite element method with mesh adaptivity for computing vortex states in fast-rotating Bose-Einstein condensates ⋮ Efficient numerical methods for computing ground states and dynamics of dipolar Bose-Einstein condensates ⋮ Global smooth solution to a coupled Schrödinger system in atomic Bose-Einstein condensates with two-dimensional spaces ⋮ GPELab, a Matlab toolbox to solve Gross-Pitaevskii equations. I: Computation of stationary solutions ⋮ Robust and efficient preconditioned Krylov spectral solvers for computing the ground states of fast rotating and strongly interacting Bose-Einstein condensates ⋮ Time-splitting Galerkin method for spin-orbit-coupled Bose-Einstein condensates ⋮ A novel adaptive finite element method for the ground state solution of Bose-Einstein condensates ⋮ Efficiently computing vortex lattices in rapid rotating Bose-Einstein condensates ⋮ Computing multiple peak solutions for Bose-Einstein condensates in optical lattices ⋮ An analysis of Schwarz waveform relaxation domain decomposition methods for the imaginary-time linear Schrödinger and Gross-Pitaevskii equations ⋮ A finite-element toolbox for the stationary Gross-Pitaevskii equation with rotation ⋮ Newton--Noda Iteration for Computing the Ground States of Nonlinear Schrödinger Equations ⋮ A regularized Newton method for computing ground states of Bose-Einstein condensates ⋮ NUMERICAL CONTINUATION FOR NONLINEAR SCHRÖDINGER EQUATIONS ⋮ Gradient Flow Finite Element Discretisations with Energy-Based Adaptivity for Excited States of Schrödinger's Equation ⋮ On numerical methods for nonlinear singularly perturbed Schrödinger problems ⋮ Spin-density separation of spin-orbit coupled Bose-Einstein condensates under rotation ⋮ An overview of \textit{a posteriori} error estimation and post-processing methods for nonlinear eigenvalue problems ⋮ Computation of Ground States of the Gross--Pitaevskii Functional via Riemannian Optimization ⋮ Unnamed Item ⋮ Second-order flows for computing the ground states of rotating Bose-Einstein condensates ⋮ A normalized gradient flow method with attractive-repulsive splitting for computing ground states of Bose-Einstein condensates with higher-order interaction ⋮ Efficient spectral computation of the stationary states of rotating Bose-Einstein condensates by preconditioned nonlinear conjugate gradient methods ⋮ A novel domain decomposition framework for the ground state solution of Bose-Einstein condensates ⋮ High-Order Mass- and Energy-Conserving Methods for the Nonlinear Schrödinger Equation ⋮ BEC2HPC: a HPC spectral solver for nonlinear Schrödinger and rotating Gross-Pitaevskii equations. Stationary states computation ⋮ Sobolev Gradient Flow for the Gross--Pitaevskii Eigenvalue Problem: Global Convergence and Computational Efficiency ⋮ A positivity preserving iterative method for finding the ground states of saturable nonlinear Schrödinger equations ⋮ Equilibrium vortex lattices of a binary rotating atomic Bose-Einstein condensate with unequal atomic masses ⋮ Crank–Nicolson Galerkin approximations to nonlinear Schrödinger equations with rough potentials ⋮ Asymptotic estimates of the convergence of classical Schwarz waveform relaxation domain decomposition methods for two-dimensional stationary quantum waves ⋮ Simulation of coherent structures in nonlinear Schrödinger-type equations ⋮ The finite element method for computing the ground states of the dipolar Bose-Einstein condensates ⋮ Efficient SAV approach for imaginary time gradient flows with applications to one- and multi-component Bose-Einstein condensates ⋮ Computing wave functions of nonlinear Schrödinger equations: a time-independent approach ⋮ GSGPEs: a MATLAB code for computing the ground state of systems of Gross-Pitaevskii equations ⋮ Acceleration of the imaginary time method for spectrally computing the stationary states of Gross-Pitaevskii equations ⋮ Relaxation algorithm to hyperbolic states in Gross-Pitaevskii equation ⋮ Fortran programs for the time-dependent Gross-Pitaevskii equation in a fully anisotropic trap ⋮ Review Article: Mathematical Models and Numerical Methods for Spinor Bose-Einstein Condensates ⋮ Perturbation theory for Bose–Einstein condensates on bounded space domains ⋮ Energy dissipating flows for solving nonlinear eigenpair problems ⋮ Gauss-Seidel-type methods for energy states of a multi-component Bose-Einstein condensate ⋮ Numerical approximations of a nonlinear eigenvalue problem and applications to a density functional model ⋮ NUMERICAL SIMULATION OF QUANTUM STATE REDUCTION IN BOSE–EINSTEIN CONDENSATES WITH ATTRACTIVE INTERACTIONS ⋮ A basis-set based fortran program to solve the Gross-Pitaevskii equation for dilute Bose gases in harmonic and anharmonic traps ⋮ Convergence rate of dimension reduction in Bose-Einstein condensates ⋮ A finite difference continuation method for computing energy levels of Bose-Einstein condensates ⋮ A multigrid method for the ground state solution of Bose-Einstein condensates based on Newton iteration ⋮ Unnamed Item ⋮ Computing Ground States of Bose--Einstein Condensates with Higher Order Interaction via a Regularized Density Function Formulation ⋮ High-order time-splitting Hermite and Fourier spectral methods ⋮ DYNAMICS OF THE GROUND STATE AND CENTRAL VORTEX STATES IN BOSE–EINSTEIN CONDENSATION ⋮ Modeling and Computation of Bose-Einstein Condensates: Stationary States, Nucleation, Dynamics, Stochasticity ⋮ A minimisation approach for computing the ground state of Gross-Pitaevskii systems ⋮ The \(J\)-method for the Gross-Pitaevskii eigenvalue problem ⋮ Newton-based methods for finding the positive ground state of Gross-Pitaevskii equations ⋮ A continuation BSOR-Lanczos--Galerkin method for positive bound states of a multi-component Bose-Einstein condensate ⋮ Normalized Gradient Flow with Lagrange Multiplier for Computing Ground States of Bose--Einstein Condensates ⋮ Finding the global optimum of a class of quartic minimization problem
Cites Work
- Particle-inspired scheme for the Gross-Pitaevski equation: an application to Bose-Einstein condensation.
- On time-splitting spectral approximations for the Schrödinger equation in the semiclassical regime
- Numerical solution of the Gross--Pitaevskii equation for Bose--Einstein condensation
- Structure of a quantized vortex in boson systems
- Numerical Study of Time-Splitting Spectral Discretizations of Nonlinear Schrödinger Equations in the Semiclassical Regimes
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
