Adaptive artificial boundary condition for the two-level Schrödinger equation with conical crossings

DOI10.1016/j.jcp.2010.11.004zbMath1210.65155OpenAlexW2042877525MaRDI QIDQ630365

Zhiwen Zhang, Houde Han

Publication date: 17 March 2011

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

Full work available at URL: https://doi.org/10.1016/j.jcp.2010.11.004

zbMATH Keywords

finite difference methodnumerical examplesunbounded domainSchrödinger equationwindowed Fourier transformartificial boundary conditionoperator splitting methodconical crossingslocal wave numbersurface hopping method

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) PDEs in connection with quantum mechanics (35Q40)

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Cites Work

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• Local spectral time splitting method for first- and second-order partial differential equations
• Exact artifical boundary conditions for the Schrödinger equation in \(\mathbb R ^2\)
• Split local absorbing conditions for one-dimensional nonlinear Klein-Gordon equation on unbounded domain
• Monte Carlo sampling of Wigner functions and surface hopping quantum dynamics
• Numerical solution of problems on unbounded domains. A review
• Unconditionally stable discretization schemes of non-reflecting boundary conditions for the one-dimensional Schrödinger equation.
• Exact and approximating boundary conditions for the parabolic problems on unbounded domains
• Absorbing boundary conditions for diffusion equations
• Adaptive absorbing boundary conditions for Schrödinger-type equations: Application to nonlinear and multi-dimensional problems
• Absorbing boundary conditions for nonlinear scalar partial differential equations
• Construction and validation of a rigorous surface hopping algorithm for conical crossing
• Exact nonreflecting boundary conditions for one-dimensional cubic nonlinear Schrödinger equations
• Absorbing boundary conditions for one-dimensional nonlinear Schrödinger equations
• An Eulerian Surface Hopping Method for the Schrödinger Equation with Conical Crossings
• Numerical solutions of Schrödinger equations in ℝ3
• Absorbing Boundary Conditions for Difference Approximations to the Multi-Dimensional Wave Equation
• Asymptotic Boundary Conditions and Numerical Methods for Nonlinear Elliptic Problems on Unbounded Domains
• Absorbing Boundary Conditions for the Numerical Simulation of Waves
• Molecular propagation through electron energy level crossings
• Absorbing Boundary Conditions for the Schrödinger Equation
• Numerical schemes for the simulation of the two-dimensional Schrödinger equation using non-reflecting boundary conditions
• Wigner measures and codimension two crossings
• Artificial boundary conditions for one-dimensional cubic nonlinear Schrödinger equations
• On the Construction and Comparison of Difference Schemes
• Propagation through conical crossings: An asymptotic semigroup