Second-order flows for computing the ground states of rotating Bose-Einstein condensates

DOI10.1016/j.jcp.2022.111872OpenAlexW4313252793MaRDI QIDQ2683094

Yanyan Li

Publication date: 3 February 2023

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2205.00805

zbMATH Keywords

ground stateGross-Pitaevskii energy functionalinertial dynamicsrotating Bose-Einstein condensateconstrained non-convex minimizationsecond-order dissipative hyperbolic PDEs

Mathematics Subject Classification ID

Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65Mxx) Partial differential equations of mathematical physics and other areas of application (35Qxx) Time-dependent statistical mechanics (dynamic and nonequilibrium) (82Cxx)

Uses Software

• BEC2HPC

Cites Work

• Unnamed Item
• Robust and efficient preconditioned Krylov spectral solvers for computing the ground states of fast rotating and strongly interacting Bose-Einstein condensates
• Efficiently computing vortex lattices in rapid rotating Bose-Einstein condensates
• Numerical analysis of nonlinear eigenvalue problems
• Efficient and spectrally accurate numerical methods for computing ground and first excited states in Bose-Einstein condensates
• A minimisation approach for computing the ground state of Gross-Pitaevskii systems
• A regularized Newton method for computing ground states of Bose-Einstein condensates
• Efficient spectral computation of the stationary states of rotating Bose-Einstein condensates by preconditioned nonlinear conjugate gradient methods
• Gross-Pitaevskii theory of the rotating Bose gas
• Ground-state solution of Bose--Einstein condensate by directly minimizing the energy functional
• Mathematical theory and numerical methods for Bose-Einstein condensation
• The \(J\)-method for the Gross-Pitaevskii eigenvalue problem
• Convergence rates of first- and higher-order dynamics for solving linear ill-posed problems
• Efficient and accurate gradient flow methods for computing ground states of spinor Bose-Einstein condensates
• Gradient flow finite element discretizations with energy-based adaptivity for the Gross-Pitaevskii equation
• Efficient SAV approach for imaginary time gradient flows with applications to one- and multi-component Bose-Einstein condensates
• Accelerated variational PDEs for efficient solution of regularized inversion problems
• Fast convergence of inertial dynamics and algorithms with asymptotic vanishing viscosity
• Ground, symmetric and central vortex states in rotating Bose-Einstein condensates
• A finite element method with mesh adaptivity for computing vortex states in fast-rotating Bose-Einstein condensates
• Optimizing Schrödinger Functionals Using Sobolev Gradients: Applications to Quantum Mechanics and Nonlinear Optics
• A Differential Equation for Modeling Nesterov's Accelerated Gradient Method: Theory and Insights
• A New Sobolev Gradient Method for Direct Minimization of the Gross–Pitaevskii Energy with Rotation
• Convergence Rates of Inertial Primal-Dual Dynamical Methods for Separable Convex Optimization Problems
• THE HEAVY BALL WITH FRICTION METHOD, I. THE CONTINUOUS DYNAMICAL SYSTEM: GLOBAL EXPLORATION OF THE LOCAL MINIMA OF A REAL-VALUED FUNCTION BY ASYMPTOTIC ANALYSIS OF A DISSIPATIVE DYNAMICAL SYSTEM
• A Two-Parameter Continuation Method for Rotating Two-Component Bose-Einstein Condensates in Optical Lattices
• Computation of Ground States of the Gross--Pitaevskii Functional via Riemannian Optimization
• Computing the Ground State Solution of Bose--Einstein Condensates by a Normalized Gradient Flow
• An analysis of finite-dimensional approximations for the ground state solution of Bose–Einstein condensates
• On the second-order asymptotical regularization of linear ill-posed inverse problems
• Sobolev Gradient Flow for the Gross--Pitaevskii Eigenvalue Problem: Global Convergence and Computational Efficiency
• A Preconditioned Conjugated Gradient Method for Computing Ground States of Rotating Dipolar Bose-Einstein Condensates via Kernel Truncation Method for Dipole-Dipole Interaction Evaluation
• Dynamics of Rotating Bose--Einstein Condensates and its Efficient and Accurate Numerical Computation
• Some methods of speeding up the convergence of iteration methods
• Normalized Gradient Flow with Lagrange Multiplier for Computing Ground States of Bose--Einstein Condensates
• A Class of Second-Order Geometric Quasilinear Hyperbolic PDEs and Their Application in Imaging
• A primal-dual flow for affine constrained convex optimization
• Dynamical representations of constrained multicomponent nonlinear Schrödinger equations in arbitrary dimensions
• A numerical damped oscillator approach to constrained Schrödinger equations
• BEC2HPC: a HPC spectral solver for nonlinear Schrödinger and rotating Gross-Pitaevskii equations. Stationary states computation

This page was built for publication: Second-order flows for computing the ground states of rotating Bose-Einstein condensates