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基于球摆模型的离散变分积分子算法研究 被引量:4
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作者 白龙 戈新生 《动力学与控制学报》 2013年第4期295-300,共6页
在动力学系统长时间的仿真计算中,力学系统固有的结构将影响到计算精度及稳定性.离散变分积分子能够保持力学系统的能量,动量及辛结构的守恒.结合离散变分原理,通过对系统的拉格朗日函数进行离散化以及求变分和积分的过程,可以得到力学... 在动力学系统长时间的仿真计算中,力学系统固有的结构将影响到计算精度及稳定性.离散变分积分子能够保持力学系统的能量,动量及辛结构的守恒.结合离散变分原理,通过对系统的拉格朗日函数进行离散化以及求变分和积分的过程,可以得到力学系统的离散变分积分子算法.该算法是一种递归算法,给定初始条件便可得到系统的动力学参数的时间历程.使用该原理可以构造具有完整约束的拉格朗日系统的辛-动量积分子方法.与连续算法相比,离散变分积分子算法能够直接在离散拉格朗日函数的基础上得到姿态与角速度的递推公式,而不需要复杂的迭代计算.本文研究是基于第一类拉格朗日函数的离散变分积分子算法.球摆模型是一个具有完整约束的拉格朗日系统.仿真结果表明,系统的能量值在长时间的仿真中得到保持,且计算的精度与步长的数量级呈现二次方的关系,系统角速度和姿态的仿真结果都符合球摆的运动规律. 展开更多
关键词 离散变分原理 力学积分子 拉格朗日函数 能量守恒
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Path Integral Formalism for Nondegenerate Parametric Amplifiers in Entangled State Representation
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作者 FANHong-Yi LIChao +1 位作者 LIUQiu-Yu AlfredWiinsche 《Communications in Theoretical Physics》 SCIE CAS CSCD 2005年第6期998-1002,共5页
We establish the path integral formalism for nondegenerate parametric amplifiers in the entangled state representations. Its advantage in obtaining the energy level gap of this system is analyzed.
关键词 path integral entangled states nondegenerate parametric amplifier
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On Quantum Mechanical Hankel Transform and Its Applications
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作者 FAN Hong-Yi WANG Ji-Suo 《Communications in Theoretical Physics》 SCIE CAS CSCD 2007年第2X期304-308,共5页
Based on our preceding works of how to relate the mathematical Hankel transform to quantum mechanical representation transform and how to express the Bessel equation by an operator identity in some appropriate represe... Based on our preceding works of how to relate the mathematical Hankel transform to quantum mechanical representation transform and how to express the Bessel equation by an operator identity in some appropriate representations we propose the concept of quantum mechanical Hankel transform with regard to quantum state vectors. Then we discuss its new applications. 展开更多
关键词 quantum mechanical Hankel transform entangled state integration equation
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Quantum Mechanical Correspondence of Poisson Integral Formula
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作者 范洪义 姜年权 《Communications in Theoretical Physics》 SCIE CAS CSCD 2011年第2期217-220,共4页
In this paper we set up quantum mechanical correspondence of the Poisson integral formula.We show that Poisson kernel function existing in the transformation between the continuum entangled state representation and it... In this paper we set up quantum mechanical correspondence of the Poisson integral formula.We show that Poisson kernel function existing in the transformation between the continuum entangled state representation and its induced state,i.e.the number-difference-correlated amplitude entangled state representation. 展开更多
关键词 Poisson integral formula entangled state representation quantum mechanical correspondence
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A Categorification of the Boson Oscillator
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作者 LIN Bing-Sheng WU Ke 《Communications in Theoretical Physics》 SCIE CAS CSCD 2012年第1期34-40,共7页
In this paper,we investigate the categorical description of the boson oscillator.Based on the categories constructed by Khovanov,we introduce a categorification of the Fock states and the corresponding inner product o... In this paper,we investigate the categorical description of the boson oscillator.Based on the categories constructed by Khovanov,we introduce a categorification of the Fock states and the corresponding inner product of these states.We find that there are two different categorical definitions of the inner product of the Fock states.These two definitions are consistent with each other,and the decategorification results also coincide with those in conventional quantum mechanics.We also find that there are some interesting properties of the 2-morphisms which relate to the inner product of the states. 展开更多
关键词 CATEGORIFICATION Boson oscillator Fock state Heisenberg algebra
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Necessity of Integral Formalism
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作者 陶勇 《Communications in Theoretical Physics》 SCIE CAS CSCD 2011年第10期648-654,共7页
To describe the physical reality, there are two ways of constructing the dynamical equation of field, differential formalism and integral formalism. The importance of this fact is firstly emphasized by Yang in case of... To describe the physical reality, there are two ways of constructing the dynamical equation of field, differential formalism and integral formalism. The importance of this fact is firstly emphasized by Yang in case of gauge field [Phys. Rev. Lett. 33 (1974) 44fi], where the fact has given rise to a deeper understanding for Aharonov-Bohm phase and magnetic monopole [Phys. Rev. D 12 (1975) 3846]. In this paper we shall point out that such a fact also holds in general wave function of matter, it may give rise to a deeper understanding for Berry phase. Most importantly, we shall prove a point that, for general wave function of matter, in the adiabatic limit, there is an intrinsic difference between its integral formalism and differential formalism. It is neglect of this difference that leads to an inconsistency of quantum adiabatic theorem pointed out by Marzlin and Sanders [Phys. Rev. Lett. 93 (2004) 160408]. It has been widely accepted that there is no physical difference of using differential operator or integral operator to construct the dynamical equation of field. Nevertheless, our study shows that the Schroedinger differential equation (i.e., differential formalism for wave function) shall lead to vanishing Berry phase and that the Schroedinger integral equation (i.e., integral formalism for wave function), in the adiabatic limit, can satisfactorily give the Berry phase. Therefore, we reach a conclusion: There are two ways of describing physical reality, differential formalism and integral formalism; but the integral formalism is a unique way of complete description. 展开更多
关键词 quantum adiabatic theorem integral formalism differential formalism Berry phase gauge field
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Computation of kinetic isotope effects for enzymatic reactions
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作者 GAO JiaLi 《Science China Chemistry》 SCIE EI CAS 2011年第12期1841-1850,共10页
We describe a computational approach,incorporating quantum mechanics into enzyme kinetics modeling with a special emphasis on computation of kinetic isotope effects.Two aspects are highlighted:(1) the potential energy... We describe a computational approach,incorporating quantum mechanics into enzyme kinetics modeling with a special emphasis on computation of kinetic isotope effects.Two aspects are highlighted:(1) the potential energy surface is represented by a combined quantum mechanical and molecular mechanical(QM/MM) potential in which the bond forming and breaking processes are modeled by electronic structure theory,and(2) a free energy perturbation method in path integral simulation is used to determine both kinetic isotope effects(KIEs).In this approach,which is called the PI-FEP/UM method,a light(heavy) isotope is mutated into a heavy(light) counterpart in centroid path integral simulations.The method is illustrated in the study of primary and secondary KIEs in two enzyme systems.In the case of nitroalkane oxidase,the enzymatic reaction exhibits enhanced quantum tunneling over that of the uncatalyzed process in water.In the dopa delarboxylase reaction,there appears to be distinguishable primary carbon-13 and secondary deuterium KIEs when the internal proton tautomerism is in the N-protonated or in the O-protonated positions.These examples show that the incorporation of quantum mechanical effects in enzyme kinetics modeling offers an opportunity to accurately and reliably model the mechanisms and free energies of enzymatic reactions. 展开更多
关键词 combined QM/MM path integral simulations PI-FEP/UM kinetic isotope effects and enzyme kinetics
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Phase behavior and interfacial properties of symmetric polymeric ternary blends A/B/AB
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作者 LIU XiaoHan BAI ZhiQiang +2 位作者 YANG KeDa SU JiaYe GUO HongXia 《Science China Chemistry》 SCIE EI CAS 2013年第12期1710-1721,共12页
In this paper, the phase behavior and interracial properties of symmetric ternary polymeric blends A/B/AB are studied by dissipative particle dynamics (DPD) simulations. By using the structure factor and nematic ord... In this paper, the phase behavior and interracial properties of symmetric ternary polymeric blends A/B/AB are studied by dissipative particle dynamics (DPD) simulations. By using the structure factor and nematic order parameter, we carefully characterized the diversified phases and phase transitions, and established the phase diagram of such symmetric ternary blends. It can be generally divided into four regions: disordered phase (DIS) region at high temperature, ordered lameUar phase (LAM) region, bicontinuous microemulsion (BμE) channel and phase-separated phase (2P) region at low temperature with the increase of the total volume fractions of homopolymers φn, which shows good accordance with that in previous experimental and theoretical reports. Furthermore, we calculated the elastic constants of 2P and LAM phase, and discussed the transition mechanisms from 2P and LAM to BμE phase, respectively. The results show a direct relevance between the phase transitions and the change of interfacial properties. Finally, we also demonstrate that the B,uE channel becomes narrower in lower temperature caused by the temperature dependence of interfacial properties of ternary blends. 展开更多
关键词 symmetric ternary blend phase behavior bicontinuous microemulsion dissipative particle dynamics
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