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Volume 2, Issue 1
Recent Progress in Symplectic Algorithms for Use in Quantum Systems

X. S. Liu, Y. Y. Qi, J. F. He & P. Z. Ding

Commun. Comput. Phys., 2 (2007), pp. 1-53.

Published online: 2007-02

[An open-access article; the PDF is free to any online user.]

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  • Abstract

In this paper we survey recent progress in symplectic algorithms for use in quantum systems in the following topics: Symplectic schemes for solving Hamiltonian systems; Classical trajectories of diatomic systems, model molecule A2B, Hydrogen ion H2+ and elementary atmospheric reaction N(4S)+O2(X3Σ8−)→NO(X2Π)+O(3P) calculated by means of Runge-Kutta methods and symplectic methods; the classical dissociation of the HF molecule and classical dynamics of H2+ in an intense laser field; the symplectic form and symplectic-scheme shooting method for the time-independent Schrödinger equation; the computation of continuum eigenfunction of the Schrödinger equation; asymptotic boundary conditions for solving the time-dependent Schrödinger equation of an atom in an intense laser field; symplectic discretization based on asymptotic boundary condition and the numerical eigenfunction expansion; and applications in computing multi-photon ionization, above-threshold ionization, Rabbi oscillation and high-order harmonic generation of laser-atom interaction.

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@Article{CiCP-2-1, author = {X. S. Liu, Y. Y. Qi, J. F. He and P. Z. Ding}, title = {Recent Progress in Symplectic Algorithms for Use in Quantum Systems}, journal = {Communications in Computational Physics}, year = {2007}, volume = {2}, number = {1}, pages = {1--53}, abstract = {

In this paper we survey recent progress in symplectic algorithms for use in quantum systems in the following topics: Symplectic schemes for solving Hamiltonian systems; Classical trajectories of diatomic systems, model molecule A2B, Hydrogen ion H2+ and elementary atmospheric reaction N(4S)+O2(X3Σ8−)→NO(X2Π)+O(3P) calculated by means of Runge-Kutta methods and symplectic methods; the classical dissociation of the HF molecule and classical dynamics of H2+ in an intense laser field; the symplectic form and symplectic-scheme shooting method for the time-independent Schrödinger equation; the computation of continuum eigenfunction of the Schrödinger equation; asymptotic boundary conditions for solving the time-dependent Schrödinger equation of an atom in an intense laser field; symplectic discretization based on asymptotic boundary condition and the numerical eigenfunction expansion; and applications in computing multi-photon ionization, above-threshold ionization, Rabbi oscillation and high-order harmonic generation of laser-atom interaction.

}, issn = {1991-7120}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cicp/7894.html} }
TY - JOUR T1 - Recent Progress in Symplectic Algorithms for Use in Quantum Systems AU - X. S. Liu, Y. Y. Qi, J. F. He & P. Z. Ding JO - Communications in Computational Physics VL - 1 SP - 1 EP - 53 PY - 2007 DA - 2007/02 SN - 2 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/cicp/7894.html KW - AB -

In this paper we survey recent progress in symplectic algorithms for use in quantum systems in the following topics: Symplectic schemes for solving Hamiltonian systems; Classical trajectories of diatomic systems, model molecule A2B, Hydrogen ion H2+ and elementary atmospheric reaction N(4S)+O2(X3Σ8−)→NO(X2Π)+O(3P) calculated by means of Runge-Kutta methods and symplectic methods; the classical dissociation of the HF molecule and classical dynamics of H2+ in an intense laser field; the symplectic form and symplectic-scheme shooting method for the time-independent Schrödinger equation; the computation of continuum eigenfunction of the Schrödinger equation; asymptotic boundary conditions for solving the time-dependent Schrödinger equation of an atom in an intense laser field; symplectic discretization based on asymptotic boundary condition and the numerical eigenfunction expansion; and applications in computing multi-photon ionization, above-threshold ionization, Rabbi oscillation and high-order harmonic generation of laser-atom interaction.

X. S. Liu, Y. Y. Qi, J. F. He and P. Z. Ding. (2007). Recent Progress in Symplectic Algorithms for Use in Quantum Systems. Communications in Computational Physics. 2 (1). 1-53. doi:
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