Magnus--Lanczos Methods with Simplified Commutators for the Schrödinger Equation with a Time-Dependent Potential

DOI10.1137/17M1149833zbMath1395.65102arXiv1801.06913OpenAlexW2963854584MaRDI QIDQ4564780

Pranav Singh, Arieh Iserles, Karolina Kropielnicka

Publication date: 12 June 2018

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1801.06913

zbMATH Keywords

Lie algebraSchrödinger equationtime-dependent potentialMagnus expansionlarge time stepsoscillatory potentialsanticommutatorsLanczos iterationsintegral-preservingsimplified commutators

Mathematics Subject Classification ID

Numerical methods for initial value problems involving ordinary differential equations (65L05) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Time-dependent Schrödinger equations and Dirac equations (35Q41) Numerical computation of matrix exponential and similar matrix functions (65F60)

Related Items (5)

Compact schemes for laser-matter interaction in Schrödinger equation based on effective splittings of Magnus expansion ⋮ Computing Semigroups with Error Control ⋮ Efficient multiscale methods for the semiclassical Schrödinger equation with time-dependent potentials ⋮ Efficient exponential splitting spectral methods for linear Schrödinger equation in the semiclassical regime ⋮ Solving Schrödinger equation in semiclassical regime with highly oscillatory time-dependent potentials

Cites Work

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• Effective approximation for the semiclassical Schrödinger equation
• High-order commutator-free exponential time-propagation of driven quantum systems
• Convergence of the Magnus series
• From quantum to classical molecular dynamics: Reduced models and numerical analysis.
• Low-order polynomial approximation of propagators for the time-dependent Schrödinger equation
• Semi-global approach for propagation of the time-dependent Schrödinger equation for time-dependent and nonlinear problems
• High-order commutator-free quasi-Magnus exponential integrators for non-autonomous~linear evolution equations
• New, highly accurate propagator for the linear and nonlinear Schrödinger equation
• A New Approach to Bernoulli Polynomials
• Efficient Solution of Parabolic Equations by Krylov Approximation Methods
• On the solution of linear differential equations in Lie groups
• On Krylov Subspace Approximations to the Matrix Exponential Operator
• On Magnus Integrators for Time-Dependent Schrödinger Equations
• Computing Highly Oscillatory Integrals
• Efficient methods for linear Schrödinger equation in the semiclassical regime with time-dependent potential
• Sufficient conditions for the convergence of the Magnus expansion
• On the exponential solution of differential equations for a linear operator

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