Quantum Dynamics with the Parallel Transport Gauge

DOI10.1137/18M1179304zbMath1440.65113arXiv1804.02095OpenAlexW3019024125MaRDI QIDQ5112039

Lin Lin, Dong An

Publication date: 27 May 2020

Published in: Multiscale Modeling & Simulation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1804.02095

zbMATH Keywords

Schrödinger equationdensity matrixparallel transportsingularly perturbed systemsymplectic methodtime-dependent density functional theoryadiabatic theoremvon Neumann equationquantum dynamics gauge

Mathematics Subject Classification ID

Singular perturbations in context of PDEs (35B25) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) NLS equations (nonlinear Schrödinger equations) (35Q55) Many-body theory; quantum Hall effect (81V70) Lasers, masers, optical bistability, nonlinear optics (78A60) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20) Molecular physics (81V55) Numerical methods for Hamiltonian systems including symplectic integrators (65P10) Time-dependent Schrödinger equations and Dirac equations (35Q41) Computational density functional analysis in statistical mechanics (82M36) Transport equations (35Q49)

Related Items

Parallel transport dynamics for mixed quantum states with applications to time-dependent density functional theory ⋮ Fast real-time time-dependent hybrid functional calculations with the parallel transport gauge and the adaptively compressed exchange formulation

Uses Software

• RODAS
• KELLEY
• VMD
• DGDFT

Cites Work

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• Weakly nonlinear time-adiabatic theory
• Adaptive local basis set for Kohn-Sham density functional theory in a discontinuous Galerkin framework. I: Total energy calculation
• A symplectic integration algorithm for separable Hamiltonian functions
• Adiabatic theorem without a gap condition
• Numerical integrators for quantum dynamics close to the adiabatic limit
• Adiabatic perturbation theory in quantum dynamics
• On time-splitting spectral approximations for the Schrödinger equation in the semiclassical regime
• Linear adiabatic theory. Exponential estimates
• Krylov deferred correction accelerated method of lines transpose for parabolic problems
• Elliptic Preconditioner for Accelerating the Self-Consistent Field Iteration in Kohn--Sham Density Functional Theory
• Wannier functions and ℤ2 invariants in time-reversal symmetric topological insulators
• On splitting methods for Schrödinger-Poisson and cubic nonlinear Schrödinger equations
• A First Course in the Numerical Analysis of Differential Equations
• On the Singular Limit of the Quantum-Classical Molecular Dynamics Model
• A nonlinear quantum adiabatic approximation
• Numerical Integrators for Highly Oscillatory Hamiltonian Systems: A Review
• Fourth-Order Time-Stepping for Stiff PDEs
• Dynamical Low‐Rank Approximation
• Geometric Numerical Integration
• Iterative Procedures for Nonlinear Integral Equations