相干态在量子转动中的应用(Ⅲ):群类算符的计算

众所周知,转过相同角度的所有转动属于同一类,这一点是难于彻底算出来的。通过相干态的性质以及正规乘积内积分法,我们得到了一种只与角动量算子相关的类算符有关的严格表达式。在整个计算过程中应用了角动量的Schwinger玻色子实现。

正规乘积内积分技术与广义量子转动

利用相干态和正规乘积内的积分技术,我们很简捷地导出了指数双线性型玻色算符的正规乘积展开和反正规乘积展开,这类新恒等式在统计物理和求费曼转换矩阵元以及在量子光学中有直接的应用。

转动传能中的量子干涉——干涉角和转动量子数的关系

沙国河等人在CO(A1∏(v=0)～e3∑-(v=1))体系与He, Ne 和Ar碰撞诱导转动传能中首次观测到了量子干涉效应,并测量了干涉度.从理论上进一步研究原子-双原子分子体系碰撞诱导转动传能中量子干涉效应与转动量子数以及能量间隔的关系是十分必要的.我们考虑长程相互作用势,应用一级玻恩近似和直线轨迹近似,分别计算了CO(A1∏(v=0)～e3∑-(v=1))体系和He, Ne,Ar碰撞诱导转动传能中不同转动量子数以及不同能量间隔下的干涉角,得到了干涉角随转动量子数和能量间隔的变化趋势.这些结果对设计、分析这种类型的实验有一定的指导意义.

NaH(b^3Π～A^1∑^+)-He碰撞系统转动传能量子干涉效应的研究

为了进一步理解原子双原子系统碰撞转动传能中的量子干涉效应,本文对NaH(b^3Π～A^1∑^+)-He碰撞系统进行了理论计算.本文利用一阶含时波恩近似和L-J相互作用势,建立了原子-双原子分子碰撞系统转动传能的量子干涉模型,通过本文理论可得出影响碰撞系统积分干涉角的因素,同时也得到了积分干涉角和转动量子数间的关系.此理论模型对于理解和进行分子束实验是非常重要的.

量子力学角动量算符的压缩态表象

我们注意到角动量上升、下降算符在绕第三轴的转动变换下呈现压缩变换的特性,故而对照双模压缩变换的特性寻求角动量算符的新的玻色算符实现.通过建立量子力学两体纠缠态表象后,我们发现了一类新的玻色实现,从而可以用压缩的观点来表述量子转动.我们还研究了在这种表示下角动量上升、下降算符对纠缠态表象作用的结果和应用.这说明在量子力学课堂教育中,引入纠缠态表象是必要的.按照本文的思路,还可以构建多粒子纠缠态表象并发现角动量的多模玻色实现.

超球坐标系下的转动量子力学

本文提出超球坐标系下在球对称力矩场中球形陀螺转动量子理论问题,给出球形陀螺的自由转动和超球振子模型的本征值和本征函数,继而引入与球形陀螺激发态相联系的四维宇称的概念。

量子干涉效应中干涉角和散射角的研究

利用波恩近似理论对双原子激发态转动传能进行了剖析,更深入的研究了原子分子碰撞过程中量子干涉效应相关信息.利用各项异性相互作用势和直线轨迹近似建立了新的量子干涉模型,讨论了原子与双原子分子碰撞时散射角和微分干涉角的关系,得到了干涉角和各向异性参数及转动量子数的关系.

反应物转动激发对反应H+HeH^+→H_2^++He立体动力学性质的影响

基于Ramachandran势能面,运用准经典轨线方法,研究了反应物转动激发对反应H+HeH+→H2++He立体动力学性质的影响。结果表明,反应物转动激发对反应的k-j′两矢量相关和k-k′-j′三矢量相关分布都产生了较大影响。产物分子H2+的转动极化在不同的转动激发态下呈现出不同的特征,而且极化微分反应截面对转动量子数j也非常敏感。

场效应光谱技术对瞬态分子的研究

瞬态分子通常具有不配对的电子，由于有了电子轨道角动量或电子自旋角动量而有较强的塞曼效应，因此，利用这类分子的外场效应，可以实现灵敏度很高吸收光谱测量。本文介绍两种外场调制的吸收光谱技术。一种是塞曼调制－磁旋转光谱技术，另一种是光外差－塞曼调制磁旋转光...

Differential Interference Angle of Collision-induced Rotational Energy Transfer in Na_2(A^1∑_u^+,v=8-b^3∏_(0u),v=14)-Na System

Here wc report calculation of the differential interference angles （including b≤p gild b≥p ） for singlet-triplet mixed states of Na2（A^1∑u^＋,ν=8-b^3∏0u,ν=14） system in collision with Na, in order to study the collision- induced quantum interference on rotational energy transfer in an atom-diatom system. The calculation is based on the first-order Born approximation of time-dependent perturbation theory, and the anisotropic Lennard-Jones intcraction potentials are also employed, The relationships between differential interference angle and impact parameter, including collision diameter and velocity, are obtained,

分子振转动量子计算及分子振转动纠缠

随着对于量子计算(机)的深入研究,人们相继提出了不同量子计算的模型.近年来,基于分子振-转激发态的量子计算模型受到了研究者的广泛关注.研究发现,基于分子振动和转动模式的量子计算模型可以很方便地实现多量子比特计算,并且可以获得足够长的退相干时间.同时,分子振转动量子计算的数值模拟也发现各种形式的量子逻辑门均可以获得很高的计算保真度.分子振转动模式之间的纠缠是分子振转动量子计算的一个重要资源,因此,分子振转动纠缠动力学的研究也引起了人们的兴趣.对于分子振转动量子纠缠动力学的研究能够为分子振转动量子计算的进一步研究和应用提供参考.本文对分子振转动量子计算和分子振动纠缠的研究进展做了简要综述.

Quantum Hadamard Operators and Their Decomposition Derived by Virtue of IWOP Technique

We introduce the quantum Hadamard operator in continuum state vector space and find that it can be decomposed into a single-mode squeezing operator and a position-momentum mutual transform operator. The two-mode Hadamard operator in bipartite entangled state representation is also introduced, which involves the two-mode squeezing operator and [η〉 ←→｜ξ〉 mutual transformation operator, where [η〉 and ｜ξ〉 are mutual conjugate entangled states. All the discussions are proceeded by virtue of the IWOP technique.

Collisional Quantum Interference on Rotational Energy Transfer： Relation Between Integral Interference Angle and Rotational Quantum Number in Na2（A^1∑u^＋,ν=8～b^3∏0u,ν=14）-Na System

Collisional quantum interference （CQI） on rotational energy transfer was observed in Na2（A^1∑u^＋,ν=8～b^3∏0u,ν=14） system in collision with Na [Chem. Phys. Lett. 318 （2000） 107], and the degree of the interference was measured. The integral interference angle was obtaJned through theoretical calculation. We will research the factors that have effect on collisional quantum interference on rotational energy transfer in Na2（A^1∑u^＋,ν=8～b^3∏0u,ν=14）-Na system. Basing on the time-dependent first order Born approximation, and taking into account the anlsotroplc Lennard Jones interaction potentials and ＂straight-line＂ trajectory approximation, we obtain the factors that have effect on CQI in Na2-Na system, and obtain the relation between the integral interference angle and rotational quantum number.

Understanding Rotational Mode Specificity in the O（3P）+CHD3→OH+CD3 Reaction by Simple Reactant Alignment Pictures

The mode specificity plays an important role in understanding the fundamental reaction dynamics. This work reports a theoretical study of the rotational mode specificity of the reactant CHD3(JK) in the prototypical hydrocarbon oxidation reaction O(3P)+CHD3→OH+CD3. The time-dependent quantum wave packet method combined with a seven-dimensional reduced model is employed to calculate the reaction probability on an accurate potential energy surface. The obtained reaction probability depends on the values of both K and Ktot with PKtot=K=0>PKtot=K=J>PKtot=J,K=0=PKtot=0,K=J. This observation can be well rationalized by the reactant alignment pictures. Rotational excitations of CHD3 up to the angular momentum quantum number J=4 have a very weak enhancement effect on the reaction except for the state (J=4, K=0). In addition, the rotationally excited states of CHD3 with K=0 promote the reaction more than those with K=J. The quantum dynamics calculations indicate that the K=0 enhancements are mainly caused by the contributions from the components with K=Ktot=0. The components correspond to the tumbling rotation of CHD3, which enlarges the range of the reactive initial attack angles.

Gauge Transformation and Constraint Induced Operator Ordering for Charged Rigid Planar Rotator in Uniform Magnetic Field

When the motion of a particle is constrained, excess terms exist using hermitian form of Cartesian momentum pi （i=1, 2,3） in usual kinetic energy （1/2/μ）∑ pi^2 , and the correct kinetic energy turns out to be （1/2μ） ∑1/ fipi f ipi, where fi are dummy factors in classical mechanics and nontrivial in quantum mechanics. In this paper the explicit form of the dummy functions fi is given for a charged rigid planar rotator in the uniform magnetic field with different gauge chosen. Under different gauges, we have different sets of dummy factors. It means that these factors do not have direct observable effect.

Deconfinement Phase Transition Including Perturbative QCD Corrections in (Proto)neutron Star Matter

Deconlinement phase transition and neutrino trapping in （proto）neutron star matter are investigated in a chiral hadronic model （also referred to as the FST model） for the hadronic phase （HP） and in the color-flavor-locked （CFL） quark model for the deconlined quark phase. We include a perturbative QCD correction parameter αs in the CFL quark matter equation of states. It is shown that the CFL quark core with K^0 condensation forms in neutron star matter with the large value of αs. If the small value of αs is taken, hyperons suppress the CFL quark phase and the liP is dominant in the high-density region of （proto）neutron star matter. Neutrino trapping makes the fraction of the CFL quark matter decrease compared with those without neutrino trapping. Moreover, increasing the QCD correction parameter as or decreasing the bag constant B and the strange quark mass ms can make the fraction of the CFL quark matter increase, simultaneously, the fraction of neutrino in protoneutron star matter increases, too. The maximum masses and the corresponding radii of （proto）neutron stars are not sensitive to the QCD correction parameter αs.

Near Resonant Electronic and Rotational Energy Transfer AB（^1∏, J）＋C（^slj）→AB（^1∏, J＇）＋C（^sl j＇）

In our previous theoretical study, the theoretical model of thecollision-induced electronic and rotational energy transfer of AB(~1Σ, J) + C(~sl_j) → AB(~1Σ,J′) + C(~sl_(j′)) was presented. To further study the collision-induced electronic and rotationalenergy transfer theoretically on AB( ~1Π, J) + C(~sl_j) → AB( ~1Π, J′) + C(~sl_(j′)), atheoretical model is presented, based on the time-dependent first-order Born approximation, takinginto account the anisotropic Lennard-Jones interaction potential and 'straight-line' trajectoryapproximation. The changing tendency of the transitional probabilities with the anisotropicparameter is discussed.

Accurate Quantum Dynamics of the Simplest Isomerization System Involving Double-H Transfer

We perform accurate quantum dynamcs calculations on the isomerization of vinylidene-acetylene.Large-scale parallel computations are accomplished by an efficient theoretical scheme developed by our group,in which the basis functions are customized for the double-H transfer process.The A_(1)' and B_(2)'' vinylidene and delocalization states are obtained.The peaks recently observed in the cryo-SEVI spectra are analyzed,and very good agreement for the energy levels is achieved between theory and experiment.The discrepancies of energy levels between our calculations and recent experimental cryo-SEVI spectra are of similar magnitudes to the experimental error bars,or≤30 cm^(-1) excluding those involving the excitation of the CCH_(2) scissor mode.A kind of special state,called the isomerization state,is revealed and reported,which is characterized by large probability densities in both vinylidene and acetylene regions.In addition,several states dominated by vinylidene character are reported for the first time.The present work would contribute to the understanding of the double-H transfer.

UV Photolysis of N2O Isotopomers： Isotopic Fractionations and Product Rotational Quantum State Distributions

The time-dependent quantum wave packet method is used to study the dynamics of the pho- todissociation processes for the isotopomers 14N14N16O, 14N15N16O, 15N14N16O, 15N15N16O, 14N14N17O, and 14N14N18O. In general, the computed isotopic fractionation factors derived from the absorption cross sections of five heavy isotopomers are in good agreement with the experimental results. Relative to the 14NI4N16O isotopomer, the N2 rotational state distributions for the isotopically nitrogen substituted N2O are found to be entirely shifted to higher rotational states. Similar to its isotopic fractionation factors, the N2 rotational state distributions for the asymmetric isotopomers 14N15N16O and 15N14N16O are found to be observably different.

Calculation of Partition Function of QCD at Finite Chemical Potential

In equilibrium statistical field theory, the partition function has fundamental importance. In this paper we propose a direct and general method for calculating the partition function and equation of state of QCD at finite chemical potential. It is found that the partition function is totally determined by the dressed quark propagator at finite chemical potential up to a multiplicative constant. From this a criterion for the phase transition between the Nambu and the Wigner phases is obtained. This general method is applied to two specific cases： the free quark theory and QCD with a model dressed quark propagator having confinement features. In the first case, the standard Fermi distribution at T = 0 is reproduced. In the second case, we apply the conclusion in previous works to obtain the dressed quark propagator at finite chemical potential and find the unphysical result that the baryon number density vanishes for all values of chemical potential. The reason for this result is discussed.