A Bloch Decomposition–Based Split‐Step Pseudospectral Method for Quantum Dynamics with Periodic Potentials

DOI10.1137/060652026zbMath1136.65093arXiv1205.0393OpenAlexW1981857442MaRDI QIDQ5453550

Christof Sparber, Zhongyi Huang, Shih Jin, Peter Alexander Markowich

Publication date: 3 April 2008

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1205.0393

zbMATH Keywords

algorithm stability convergence numerical examples semiclassical asymptotics Schrödinger equation step size control Hamiltonian operator time-splitting spectral method Bloch decomposition lattice potential

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) PDEs in connection with quantum mechanics (35Q40) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20) Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs (65M50) Homogenization in context of PDEs; PDEs in media with periodic structure (35B27)

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