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Behaviors and high-order harmonic generation for short-range model potential in the intense laser field by using the symplectic algorithm

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自然科学进展(英文版) 2004年第7期14卷 573-581页

作者： Liu Xueshen QI Yueying HUA Wei DING Peizhu Institute of Atomic and Molecular Physics Jilin University Changchun 130012China

The asymptotic boundary condition to solve the time-dependent Schr dinger equation for a short-range model potential in an- intense laser field is presented. The condition is obtained by means of the asymptotic behavior of the short-rang emodel in the sufficiently large distance and Fourier transformation, and then the time-dependent Schr dinger equation is discretized into an inhomogeneous linear canonical equation. The inhomogeneous linear canonical equation is solved using the symplectic algorithm. The wavefunctions,time-calculatedevolution of the population on the bound state, and the high-orderharmonicgeneration verify that our numerical method is reasonable and effective.

关键词： asymptotic boundary condition high-order harmonic generation symplectic algorithm

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Plasma photonic crystals numerical and filter characteristics analysis based on symplectic algorithm

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OPTIK 2014年第17期125卷 4762-4765页

作者： Yang, Hong Wei Yang, Ze kun Liu, Han Bin Wang, Guang Nanjing Agr Univ Dept Phys Nanjing 210095 Jiangsu Peoples R China Xidian Univ Sch Comp Sci & Technol Xian 710071 Peoples R China Univ Elect Sci & Technol China Dept Comp Chengdu 611731 Peoples R China Southeast Univ State Key Lab Millimeter Waves Nanjing 210096 Jiangsu Peoples R China

From the Maxwell equation, the method of symplectic finite-difference time-domain is applied in analyzing one-dimensional plasma photonic crystal. The propagation process of electromagnetic pulse in one-dimensional vacuum plasma photonic crystal structure is simulated by symplectic algorithm discrete in 2nd order time 2nd order space (T2S2), and 2nd order time 4th order space (T2S4) respectively. Then, from the perspective of frequency domain, the reflection coefficient of the plasma vacuum photonic crystals is analyzed. The results show that the symplectic finite-difference time-domain method is accuracy and correctness. In the end, the filter characteristics of the plasma photonic crystals (PPCs) are analyzed in different thickness of plasma. (C) 2014 Elsevier GmbH. All rights reserved.

关键词： Plasma Photonic crystals symplectic algorithm Hamilton system Reflection coefficient

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Continuum eigen-functions of 1-D time-independent Schrodinger equation solved by symplectic algorithm

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INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY 2005年第1期101卷 21-26页

作者： Qi, YY Liu, XS Ding, PZ Jilin Univ Inst Atom & Mol Phys Changchun 130012 Peoples R China

We present the symplectic algorithm for solving the continuum eigen-functions of 1-dimensional (1D) time-independent Schrodinger equation, which keeps Wronskian conservation of linearly independent continuum eigen-functions. This symplectic algorithm has been applied to the computation of the linearly independent continuum eigen-functions of both 1D soft-coulomb potential and Poshl-Teller short-range potential as well as the radial continuum eigen-functions of hydrogen atom. The numerical results using the symplectic algorithm are in agreement with the existing theories. (C) 2004 Wiley Periodicals, Inc.

关键词： continuum eigen-functions symplectic algorithm time-independent Schrodinger equation Wronskian

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Ionization of 1-D model atom in an intense laser field based on asymptotic boundary conditions and symplectic algorithm

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JOURNAL OF MATHEMATICAL CHEMISTRY 2006年第1期39卷 133-149页

作者： Qi, YY Liu, XS Liu, XY Ding, PZ Jiaxing Univ Sch Elect Engn Jiaxing 314001 Peoples R China Jilin Univ Inst Atom & Mol Phys Changchun 130012 Peoples R China NE Normal Univ Dept Math Changchun 130024 Peoples R China

In this paper the asymptotic boundary condition (ABC) of 1-D model atom in the intense laser field at the spatial sufficiently far distance is presented using Fourier transformation on the condition that the initial state is local and the atomic potential in the model falls off rapidly. On the basis of this ABC, the symplectic algorithm is developed for computing the model atom in the intense laser field. The ABC and symplectic algorithm are applied to compute the ionization behaviors for 1-D Poschl-Teller short-range potential. The numerical results illustrate that the ABC and the symplectic algorithm presented are reasonable and effective for 1-D model atom in the intense laser field.

关键词： asymptotic boundary condition symplectic algorithm 1-D Poschl-Teller short-range potential ionization probability

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Computation of quasiclassical trajectories by symplectic algorithm for the N(⁴S) + O₂(X³Σ_g^-) → NO(X²Π) + O(³P) reaction system

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JOURNAL OF MATHEMATICAL CHEMISTRY 2005年第2期37卷 127-138页

作者： He, JF Hua, W Liu, XS Ding, PZ Jilin Univ Inst Atom & Mol Phys Changchun 130012 Jilin Peoples R China

Computation of quasiclassical trajectories for the N(S-4) + O-2(X(3)Sigma(g) over bar). NO(X(2)Pi) +O(P-3) atmospheric reaction system, based on a new ground potential energy surface reported by R. Sayos et al., has been performed in this work by means of both the fourth-order explicit symplectic algorithm (S4) and the fourth-order Runge-Kutta scheme (RK4), and then computed results of two schemes are compared. It is shown that RK4 cannot preserve energy conservation and symplectic structure of the reaction system, which results in the bad veracity of the trajectory calculation. RK4 cannot rightly reflect both the colliding mode and the reaction mode of the trajectories. Moreover, the amplitudes of vibration of the reactant molecule and the product molecule become gradually small with the time increasing, and their rotation-vibrational levels in fact vary during the integration. For these reasons, RK4 cannot assure the accuracy of the quasiclassical trajectory (QCT) study of the atmospheric reaction. However, S4 maintains these characteristics and can actually describe the circumstance of the reaction system. S4 is better than RK4 is prospective in the QCT study of the chemical reaction.

关键词： symplectic algorithm quasiclassical trajectory chemical reaction

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The enhancement of efficiency of high-order harmonic in intense laser field based on asymptotic boundary conditions and symplectic algorithm

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JOURNAL OF MATHEMATICAL CHEMISTRY 2006年第3-4期39卷 451-463页

作者： Zhang, Chunli Liu, Xueshen Ding, Pezhu Qi, Yueying Jilin Univ Inst Atom & Mol Phys Changchun 130012 Peoples R China Jiaxing Univ Sch Elect Engn Jiaxing 314001 Peoples R China

Asymptotic boundary condition (ABC) of laser-atom interaction presented recently is applied to transform the initial value problem of the time-dependent Schradinger equation (TDSE) in infinite space into the initial and boundary value problem in the finite space, and then the TDSE is discretized into linear canonical equations by substituting the symmetry difference quotient for the 2-order partial derivative. The canonical equation is solved by symplectic algorithm. The ground state and the equal weight coherent superposition of the ground state and the first excited state have been taken as the initial conditions, respectively, while we calculate the population of bound states, the evolution of average distance and the high-order harmonic generation (HHG). The conversion efficiency of HHG can be enhanced by initial coherent superposition state and moderate laser intensities.

关键词： asymptotic boundary condition symplectic algorithm high-order harmonic generation superposition state

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A quasi-dynamic model and a symplectic algorithm of super slender Kirchhoff rod

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International Journal of Modeling, Simulation, and Scientific Computing 2017年第3期8卷 285-295页

作者： Dandan Yang Jianfei Huang Weijia Zhao School of Mathematical Science Huaiyin Normal University Jiangsu Huaian 223300 P.R.China College of Mathematical Sciences Yangzhou University Yangzhou 225002P.R.China College of Mathematics Qingdao University Qingdao 266071P.R.China

Recently the Kirchhoff rod and the methods of dynamical analogue have been widely used in modeling *** features of a DNA such as its super slender and super large deformation raise new challenges in modeling and numerical simulations of a Kirchhoff *** this paper,Euler parameters are introduced to set up the quasi-Hamilton system of an elastic rod,then a symplectic algorithm is applied in its numerical ***,a simplified surface model of the rod is given based on the hypothesis of rigid cross-section.

关键词： Kirchhoff rod euler parameters quasi-hamilton system symplectic algorithm surface equation

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A numerical study of the orbits of near earth asteroids with symplectic algorithm

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CHINESE ASTRONOMY AND ASTROPHYSICS 1999年第1期23卷 108-119页

作者： Liu, L Ji, JH Liao, XH Nanjing Univ Dept Astron Nanjing 210008 Peoples R China

We use an improved explicit symplectic algorithm and the nested RKF7(8) integrator to study numerically the orbital evolution in 43 numbered near-Earth asteroids. Post-newtonian effect is included in the dynamical model, and we consider particularly the prospect of applying symplectic algorithm in the orbital study of asteroids and its effectiveness in case of close approach to a major planet.

关键词： near-Earth asteroids orbital evolution symplectic algorithm

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The use of symplectic algorithm in the computation of Lyapunov characteristic numbers

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Chinese Astronomy and Astrophysics 1993年第4期17卷 449-452页

作者： Liao Xin-hao Zhao Chang-yin Liu Lin Department of Astronomy Nanjing University Nanjing 210008 China

关键词： Lyapunov characteristic number symplectic algorithm

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Pseudospectral method with symplectic algorithm for he solution of time-dependent Schr(o)dinger equations

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中国物理（英文版） 2007年第7期16卷 1822-1826页

作者： Bian Xue-Bin Qiao Hao-Xue Shi Ting-Yun State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics Wuhan Institute of Physics and Mathematics Chinese Academy of Sciences Wuhan 430071 China Graduate School of the Chinese Academy of Sciences Beijing 100049 China Department of Physics Wuhan University Wuhan 430072 China State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics Wuhan Institute of Physics and Mathematics Chinese Academy of Sciences Wuhan 430071 China

A pseudospectral method with symplectic algorithm for the solution of time-dependent Schr(o)dinger equations(TDSE) is introduced. The spatial part of the wavefunction is discretized into sparse grid by pseudospectral method and the time evolution is given in symplectic scheme. This method allows us to obtain a highly accurate and stable solution of TDSE. The effectiveness and efficiency of this method is demonstrated by the high-order harmonic spectra of one-dimensional atom in strong laser field as compared with previously published work. The influence of the additional static electric field is also investigated.

关键词： pseudospectral method symplectic algorithm high-order harmonic generation

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