Newton-Leibniz integration for ket-bra operators in quantum mechanics and derivation of entangled state representations

Newton-Leibniz integration rule only applies to commuting functions of continuum variables, while operators made of Dirac’s symbols (ket versus bra, e.g., |q〉〈q| of continuous parameter q) in quantum mechanics are usually not commutative. Therefore, integrations over the operators of type |〉〈| cannot be directly performed by Newton-Leibniz rule. We invented an innovative technique of integration within an ordered product (IWOP) of operators that made the integration of non-commutative operators possible. The IWOP technique thus bridges this mathematical gap between classical mechanics and quantum mechanics, and further reveals the beauty and elegance of Dirac’s symbolic method and transformation theory. Various applications of the IWOP technique, including constructing the entangled state representations and their applications, are presented.     

Nuclear Quadrupole Coupling Constants of Chlorine and Microwave Spectrum, Structure, and ab Initio Calculation of 1-Chloro-1,1,2-trifluoroethane

The microwave spectrum of the ³⁵Cl and ³⁷Cl isotopic species of 1-chloro-1,1,2-trifluoroethane (HCFC-133b) has been investigated in the frequency region 10 to 50 GHz using a Stark modulation microwave spectrometer. A pulsed jet Fourier transform microwave spectrometer was also used for the measurement of hyperfine splittings. A least-squares analysis of the observed b-type Q- and R-branch transition frequencies gave rotational and centrifugal distortion constants and components of the chlorine nuclear quadrupole coupling constant tensors in the principal axes system as follows: A=4625.161 (3) MHz, B=2004.127 (2) MHz, C=1875.813 (2) MHz, Δ_J=0.144 (9) kHz, Δ_JK=1.0748 (8) kHz, Δ_K=1.57 (1) kHz, δ_J=0.01376 (4) kHz, δ_K=−0.146 (4) kHz, χ_aa=−57.958 (10) MHz, χ_bb=21.231 (11) MHz, and χ_cc=36.727 (11) MHz for ³⁵ClCF₂CH₂F species, and A=4607.684 (6) MHz, B=1960.565 (2) MHz, C=1834.823 (2) MHz, Δ_J=0.106 (7) kHz, Δ_JK=1.022 (3) kHz, Δ_K=1.48 (1) kHz, δ_J=0.0142 (2) kHz, δ_K=−0.18 (2) kHz, χ_aa=−46.268 (11) MHz, χ_bb=17.319 (13) MHz, and χ_cc=28.950 (13) MHz for ³⁷ClCF₂CH₂F species. The structural parameters are calculated from the observed six rotational constants by assuming the partial structure of ab initio calculation. The electronic properties of the C-Cl bond are evaluated from the observed nuclear quadrupole constants of chlorine. These molecular properties are compared with those of other related molecules.     

不连续不可逆二维映象的动力学特性

总结两个保守映象不可逆地分段连续链接(称为类耗散系统)以及一个保守映象与一个耗散映象不可逆地分段连续链接(称为半耗散系统)情况下得到的五项共同动力学特征：不连续边界象集构成的随机网成为唯一的混沌轨道；由于某些相点具有两个逆象而导致的相空间塌缩(类耗散)；由于系统的不连续不可逆性质而出现的胖分形禁区网；在具有吸引子共存时占据不连续边界象集随机网和胖分形禁区网区域的点滴状吸引域以及由此导致的吸引子不可预言性；即使在传统强耗散存在的情况下点滴状吸引域仍由类耗散机制主宰.以一个累积-触发电路为例，说明这五项系统动 关键词： 随机网 禁区网 点滴状吸引域     

基于ROI编码的干涉超光谱图像近无损压缩

针对干涉超光谱成像仪所成图像的特点，提出了一种基于ROI（Region of Interest，感兴趣区域）编码的干涉超光谱图像序列压缩方法.利用帧内差值变换，结合矩形ROI编码，在提高遥感图像压缩比的同时，使压缩后的重建图像质量达到近无损的技术要求.实验结果表明，这种压缩方法在干涉超光谱图像压缩中当相对光谱二次误差为2.04％时，干涉图像的压缩比达到9.66∶1.     

宽带膜厚实时监控过程中膜层折射率的确定方法

为了准确计算出镀膜过程中每层膜的折射率，介绍了实时监控过程中确定膜层折射率的2种方法：一种是由实测的透射比光谱直接反算出膜层的折射率；另一种是用最小二乘法的优化算法实时拟合折射率。试验结果表明：在线反算适合单点监控，所得折射率误差小于2%。然而在实际镀膜过程中,由于宽带内膜层参数误差较大,一般大于25%。为此，采用最小二乘法拟合，即在整个宽光谱范围内采集每个波长点的信息，所得结果误差很小，一般都在2％～5%之间,有时可达到10%,在很大程度上提高了实际镀膜时膜厚监控的精度。     

Assisted Cloning and Orthogonal Complementing of an Arbitrary Unknown Two-Qubit Entangled State

Based on A.K. Pati‘s original idea [Phys. Rev. A 61 (2000) 022308] on single-qubit-state-assisted clone, very recently Zhan has proposed two assisted quantum cloning protocols of a special class of unknown two-qubit entangled states [Phys. Lett. A 336 (2005) 317]. In this paper we further generalize Zhan‘s protocols such that an arbitrary unknown two-qubit entangled state can be treated.     

Fuzzy convex sets in median algebras

The fuzzification of convex sets in median algebras is considered, and some of their properties are investigated. A characterization of finite valued fuzzy convex set is given.     

U：CaF2晶体的分凝特性与光谱性质

应用TGT法生长了直径为75mm的U：CaF2晶体，宏观上透明完整.应用公式K0=Cs/Cl计算了U在CaF2晶体中的分凝系数等于0.53.应用溶质分布一般公式Cs=K0C0(1-g)K0-1，计算U的浓度分布与测量值，数值符合说明晶体生长过程接近平衡状态.分析不同条件下生长的U: CaF2晶体的晶胞参数和吸收光谱，结果表明生长气氛决定U的价态及电荷补偿机理：无PbF2存在的条件下，U为+4价，晶体呈绿色；PbF2的加入起到氟化去氧作用，U倾向于以离子半径最接近于Ca2+的U3+存在，晶体呈红色.从晶体生长开始到结束的部位，U3+:CaF2晶体吸收光谱的峰位不变，峰强呈现与U浓度相同的增加趋势.U3+:CaF2晶体外层厚约5mm处呈黄色，含有U3+和U2+的混合价态离子，其原理是石墨坩埚的还原作用通过单质铅，使部分的U3+进一步还原成了U2+. 关键词： 铀 氟化钙晶体 分凝系数 晶胞参数     

Co-P非晶态合金电子性质和局域结构的理论研究

根据Co P非晶态合金结构的短程有序和结构中可能存在P -P相互作用的实验事实 ,选择了单磷原子簇模型ConP(n =1～ 5 )和双磷原子簇模型ConP2 (n =1～ 4 ) ,用密度泛函理论方法对其进行计算 .结果表明 ,在单磷Co2 P( 2 ) 、Co3 P( 1) 及Co4P( 2 ) 模型体系中 ,Co原子供给P原子电子 ,与电负性规则一致 ,同时Co和P之间具较强化学作用 ,可以形成稳定的原子簇 ;而在双磷和单磷原子簇Co5P( 1) 模型体系中 ,形成的原子簇不稳定 ,采用单磷Co2 P( 2 ) 、Co3 P( 1) 及Co4P( 2 ) 模型能较好地反映Co P非晶态合金的结构特点 .