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Compact splitting symplectic scheme for the fourth-order dispersive schrodinger equation with Cubic-Quintic nonlinear term

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International Journal of Modeling, Simulation, and Scientific Computing 2019年第2期10卷 142-155页

作者： Lang-Yang Huang Zhi-Feng Weng Chao-Ying Lin Fujian Province University Key Laboratory of Computational Science School of Mathematical SciencesHuaqiao University Quanzhou 362021P.R.China Key Laboratory of Applied Mathematics(Putian University) Fujian Province University Fujian Putian 351100P.R.China

Combining symplectic algorithm,splitting technique and compact method,a compact splitting symplectic scheme is proposed to solve the fourth-order dispersive schr¨odinger equation with cubic-quintic nonlinear *** scheme has fourth-order accuracy in space and second-order accuracy in *** discrete charge conservation law and stability of the scheme are *** examples are given to confirm the theoretical results.

关键词： Symplectic scheme schr¨odinger equation compact splitting method conservation law

Quantum enigma hidden in continuum mechanics

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Applied Mathematics and Mechanics(English Edition) 2017年第1期38卷 39-56页

作者： Heng XIAO Shanghai Institute of Applied Mathematics and Mechanics Shanghai UniversityShanghai 200072China

It is reported that there exist deformable media which display quantum effects just as quantum entities do. As such, each quantum entity usually treated as a point particle may be represented by a deformable medium, the dynamic behavior of which is prescribed by four dynamic state variables, including mass density, velocity, internal pressure, and intrinsic angular momentum. In conjunction with the finding of the characteristic equation characterizing the physical nature of such media, it is found that a complex field quantity may be introduced to uncover a perhaps unexpected correlation, i.e., the governing dynamic equations for such media may be exactly reduced to the schrSdinger equation, from which the closed-form solutions for all the four dynamic state variables can be obtained. It turns out that this complex field quantity is just the wavefunction in the schrSdinger equation. Moreover, the dynamic effects peculiar to spin are derivable as direct consequences. It appears that these results provide a missing link in quantum theory, in the sense of disclosing the physical origin and nature of both the wavefunction and the wave equation. Now, the inherent indeterminacy in quantum theory may be rendered irrelevant. The consequences are explained for certain long-standing fundamental issues.

关键词： quantum entity deformable medium nonlinear dynamic equation new interpretation schr¨odinger equation

A Numerical Study of Quantum Decoherence

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Communications in Computational Physics 2012年第6期12卷 85-108页

作者： Riccardo Adami Claudia Negulescu Dipartimento di Matematica e Applicazioni Universita di Milano Bicoccavia R.Cozzi5320125 MilanoItaly CMI/LATP(UMR 6632) Universit´e de Provence39rue Joliot Curie13453 Marseille Cedex 13France

The present paper provides a numerical investigation of the decoherence effect induced on a quantum heavy particle by the scattering with a light *** time dependent two-particle schr¨odinger equation is solved by means of a time-splitting *** damping undergone by the non-diagonal terms of the heavy particle density matrix is estimated numerically,as well as the error in the Joos-Zeh approximation formula.

关键词： Quantum mechanics schr¨odinger equation heavy-light particle scattering interference decoherence numerical discretization numerical analysis splitting scheme

Recent Progress in Symplectic Algorithms for Use in Quantum Systems

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Communications in Computational Physics 2007年第1期2卷 1-53页

作者： Xue-Shen Liu Yue-Ying Qi Jian-Feng He Pei-Zhu Ding Institute of Atomic and Molecular Physics Jilin UniversityChangchun 130012P.R.China. School of Electrical Engineering Jiaxing UniversityJiaxing 314001P.R.China. Department of Physics School of ScienceBeijing Institute of TechnologyBeijing 100081P.R.China.

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 H+2 and elementary atmospheric reaction N(4S)+O2(X 3Σ−g)→NO(X 2Π)+O(3P)calculated by means of Runge-Kutta methods and symplectic methods;the classical dissociation of the HF molecule and classical dynamics of H+2 in an intense laser field;the symplectic form and symplectic-scheme shooting method for the time-independent schr¨odinger equation;the computation of continuum eigenfunction of the schr¨odinger equation;asymptotic boundary conditions for solving the time-dependent schr¨odinger 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.

关键词： Quantum system symplectic algorithm classical trajectory schr¨odinger equation intense laser field.