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GENERALIZED canonical transformation AND SYMPLECTIC ALGORITHM OF THE AUTONOMOUS BIRKHOFFIAN SYSTEMS

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Applied Mathematics and Mechanics(English Edition) 2002年第9期23卷 1029-1034页

作者：张兴武武际可朱海平黄克服 Department of Mechanics and Engineering Science Peking UniversityBeijing 100871P R China

The Birkhoff systems are the generalization of the Hamiltonian systems. Generalized canonical transformations are studied. The symplectic algorithm of the Hamiltonian systems is extended into that of the Birkhofflan systems. Symplectic differential scheme of autonomous Birkhoffian systems vas structured and discussed by introducing the Kailey transformation.

关键词： Birkhoffian system sympletic algorithm canonical transformation

canonical transformations and Poisson Theory for Dynamics with Non-Standard Lagrangians

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Wuhan University Journal of Natural Sciences 2024年第2期29卷 106-116页

作者： ZHU Lin ZHANG Yi School of Mathematical Sciences Suzhou University of Science and TechnologySuzhou 215009JiangsuChina School of Civil Engineering Suzhou University of Science and TechnologySuzhou 215011JiangsuChina

The canonical transformation and Poisson theory of dynamical systems with exponential,power-law,and logarithmic non-standard Lagrangians are studied,*** criterion equations of canonical transformation are established,and four basic forms of canonical transformations are *** dynamic equations with non-standard Lagrangians admit Lie algebraic *** this,we es-tablish the Poisson theory,which makes it possible to find new conservation laws through known conserved *** examples are put forward to demonstrate the use of the theory and verify its effectiveness.

关键词： non-standard Lagrangians dynamical equations canonical transformation Poisson theory

A Quantum Dynamical Mode for the Control of Decoherence

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Communications in Theoretical Physics 2005年第1期43卷 59-64页

作者： HuangWan-Xia WangQin-Mou InstituteofPhysicsDepartmentandElectronicInformation AnhuiNormalUniversityWuhu241000China

We present a quantum measurement model where the meter is taken to be a squeezed reservoir. life realize decoherence in macroscopic limits using Bogoliubov transformation, and this kind of system-meter coupling has a ... 详细信息

关键词： coherent states displace operators squeezing operators canonical transformation decoherence

Boundedness of Solutions in Asymmetric Oscillations via the Twist Theorem

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Acta Mathematica Sinica,English Series 2001年第2期17卷 313-318页

作者： Yi Qian WANG Institute of Mathematics. Academy of Mathematics and Systems Sciences. Chinese Academy of Science, Beijing 100080 P. R. China Institute of Mathematics Academy of Mathematics and Systems Sciences Chinese Academy of Science Beijing 100080 P. R. China

In this paper we consider the boundedness of all the solutions for the equation x'+ax^+ -bx^-=f(t). where f(t) is a smooth 2π-periodic function, a and b are positive constants (a≠b).

关键词： Boundedness Asymmetric canonical transformation Twist theorem

Boundedness of semilinear Duffing equations with singularity

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Frontiers of Mathematics in China 2014年第6期9卷 1427-1452页

作者： Xiumei XING Lei JIAO School of Mathematics and Statistics YiLi Normal University Yining 835000 China School of Science Nanjing University of Science and Technology Nanjing 210094 China

We prove the boundedness of all solutions for the equation x＂＋ V＇（x） = DxG（x,t）, where V（x） is of singular potential, i.e., limx→-1 Y（x） = ∞, and G（x, t） is bounded and periodic in t. We give sufficien... 详细信息

关键词： Hamiltonian system repulsive singularity boundedness ofsolutions canonical transformation Moser's small twist theorem

Phase Space Path Integral Method for Problem of Obtaining Propagator of a Particle with a Force Quadratic in Velocity

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Communications in Theoretical Physics 2006年第2期45卷 259-261页

作者： GU Zhi-Yu HUANG Bo-Wen QIAN Shang-Wu physics Department Capital Normal University Beijing 100037 China physics Department Peking University Beijing 100871 China

This article uses the phase space path integral method to find the propagator for a particle with a force quadratic in velocity. Two specific canonical transformations has been used for this purpose.

关键词： phase space path integral propagator canonical transformation

A CALCULATION METHOD TO THE PERTURBATION OF A SATELLITE CAUSED BY THE GRAVITATION FIELD OF THE EARTH

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Applied Mathematics and Mechanics(English Edition) 1997年第2期18卷 163-171页

作者：郑文虎 Department of Physics Xichang Teacher's College Xichang P. R. China

In this paper, with the application of the Delauney variables, according to the Hamilton equations, the influence on the perturbation of a satellite exerted by the gravitational force of the earth through canonical transformation has been found out. As a result, the equation about how the position and velocity of the satellite vary with time is deduced.

关键词： gravitation field Hamilton equation perturbation canonical transformation

Variable Frequency Harmonic Oscillator in an Electromagnetic Field

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Communications in Theoretical Physics 2004年第1期41卷 45-47页

作者： HUANGBo-Wen WANGJing-Shan GUZhi-Yu QIANShang-Wu PhysicsDepartment CapitalNormalUniversityBeijing100037China physicsDepartment NewJerseyInstituteofTechnologyNewarkNJ07201USA physicsDepartment PekingUniversityBeijing100871China

The invariant, propagator, and wavefunction for a variable frequency harmonic oscillator in an electromagnetic field are obtained by making a specific coordinate transformation and by using the method of phase space path integral method. The probability amplitudes for a dissipative harmonic oscillator in the time varying electric field are obtained.

关键词： invariant propagator canonical transformation phase space path integral variable frequency harmonic oscillator

Double-wave description of mesoscopic resistance-inductance-capacitance coupled circuit with power source

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Chinese Physics B 2003年第12期12卷 1360-1365页

作者：张寿朱爱东金哲李哲奎潘淑梅赵永芳井孝功千正男苏文辉 CenterfortheCondensed-MatterScienceandTechnology HarbinInstituteofTechnologyHarbin150001Ghina DepartmentofPhysics CollegeofScienceandEngineeringYanbianUniversityYanji133002China DepartmentofPhysics NortheastNormalUniversityChangchun130000China

Quantum fluctuations in the mesoscopic capacitance-inductance-resistance coupled circuit with a power source are investigated using canonical transformation and a double wavefunction. We confirm that the fluctuations are not influenced by the power source. As a new method, the double wavefunction describes a single system of the coupled circuit, whereas the single wavefunction describes a quantum ensemble.

关键词： mesoscopic circuit double wavefunction canonical transformation