Frozen Gaussian approximation with surface hopping for mixed quantum-classical dynamics: A mathematical justification of fewest switches surface hopping algorithms

DOI10.1090/mcom/3310zbMath1478.65007arXiv1602.06459OpenAlexW2963874414MaRDI QIDQ4640319

Zhennan Zhou, Jian-feng Lu

Publication date: 17 May 2018

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1602.06459

zbMATH Keywords

Schrödinger equationGaussian approximationpath integral stochastic representationsurface hopping algorithm

Mathematics Subject Classification ID

Monte Carlo methods (65C05) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) NLS equations (nonlinear Schrödinger equations) (35Q55) 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)

Related Items (11)

Observable Error Bounds of the Time-Splitting Scheme for Quantum-Classical Molecular Dynamics ⋮ Computing quantum dynamics in the semiclassical regime ⋮ Propagation of coherent states through conical intersections ⋮ Gaussian wave packet transform based numerical scheme for the semi-classical Schrödinger equation with random inputs ⋮ A Diabatic Surface Hopping Algorithm Based on Time Dependent Perturbation Theory and Semiclassical Analysis ⋮ A Quantum Kinetic Monte Carlo Method for Quantum Many-Body Spin Dynamics ⋮ The Gaussian Wave Packet Transform for the Semi-Classical Schrödinger Equation with Vector Potentials ⋮ A Surface Hopping Gaussian Beam Method for High-Dimensional Transport Systems ⋮ Propagation of wave packets for systems presenting codimension one crossings ⋮ Nonadiabatic Transitions in Multiple Dimensions ⋮ Efficient frozen Gaussian sampling algorithms for nonadiabatic quantum dynamics at metal surfaces

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