弱射频场存在下密度算符演化的描述

采用一种密度算符方法描述弱射频场存在下弱偶合自旋体系(I=1/2)的密度算符的演化,具体分析了自旋轻扰实验和显示自旋为1/2的原子核旋量特性的实验。     

描述高自旋体系的密度算符方法

提出了一种描述高自旋弱偶合体系NMR实验谱的密度算符方法,给出了高自旋体系密度算符在自旋偶合作用下的演化公式。以氘核(²D)为例,计算了重聚INEPT和同核COSY实验谱。     

描述自旋体系密度算符演化的新方法

提出一种描述自旋体系密度算符演化的新方法,可统一处理核磁共振波谱学中强、弱偶合自旋体系及弱射频场存在下密度算符的演化。具体分析一些核磁共振实验:自旋轻扰、自旋锁定、偶极耦合作用、强耦合AB和ABX自旋体系的演化。     

描述高自旋弱耦合系统的广义积算符

本文提出了Z算符与角动量积算符相结合的广义积算符,用于描述高自旋弱耦合系统NMR实验谱。给出了高自旋系统在自旋耦合作用下的演变公式,Z算符在脉冲作用下的变化公式。以氘(D)为例,计算了重聚INEPT,DEPT和同核COSY实验谱,并对计算方法作了讨论。     

自旋置换对称体系多脉冲及二维核磁共振实验的密度算符描述(Ⅱ)——多量子积算符方法

在对称化乘积算符(简称SAPO)方法基础上提出了多量子积算符(简称MQCPO)方法。改进的密度算符理论对I_nS(I=1/2,S=1/2;n为任意正整数)自旋体系多脉冲及二维核磁共振实验的描述普遍适用。MQCPO与SAPO从不同角度反映了自旋体系的对称性,故它们之间存在简单线性关系。文中给出I_n(I=1/2,n=2,3)自旋体系MQCPO的SAPO表示。MQCPO有利于自由演化过程的描述,而脉冲作用的描述则是SAPO为佳;利用MQCPO与SAPO的线性关系及SAPO笛卡儿分量的坐标轮换性质,“z”表象下脉冲作用的描述变得简单而直观。对异核谱剪辑及自旋拓扑滤波(spin topology filtration)等实验脉冲序列的分析,该方法是方便的。 关键词：     

耗散腔中两二能级原子态的自旋压缩,量子Fisher信息和最大自旋涨落

在能量耗散腔中,原子用泡利算符描述,光场用相干态描述,运用密度矩阵理论,得到了两二能级原子密度矩阵元的演化规律,分析了与单模辐射场作用过程中原子态的自旋压缩、量子Fisher信息和最大自旋涨落.结果表明:自旋压缩,大于 的最大自旋涨落可以作为量子纠缠的充分必要判据.自旋压缩, 大于 的最大自旋涨落和量子纠缠,它们互相等价.大于1的Fisher信息与它们之间没有等价关系,但可以作为自旋压缩和量子纠缠的充分判据.     

当能级间隔较小时三能级核四极共振自旋系统对脉冲的响应

用虚拟自旋-1/2算符理论考察了I=1的核四极共振自旋系统在其能级间隔较小时对1-2个脉冲的响应.由于核四极相互作用表象中的射频场与核自旋的相互作用(H_rf)包含时间,因而用Dyson时序算符来计算密度算符在H_rf作用下的演化.     

当能级间隔较小时三能级核四极共振自旋系统对脉冲的响应

用虚拟自旋—１／２算符理论考察了Ｉ＝１的核四极共振自旋系统在其能级间隔较小时对１—２个脉冲的响应．由于核四极相互作用表象中的射频场与核自旋的相互作用（Ｈｎ）包含时间．因而用Ｄｙｓｏｎ时序算符来计算密度算符在Ｈｎ作用下的演化．     

耗散腔中两二能级原子态的自旋压缩量子Fisher信息和最大自旋涨落

在能量耗散腔中,原子用泡利算符描述,光场用相干态描述,运用密度矩阵理论,得到了两二能级原子密度矩阵元的演化规律,分析了与单模辐射场作用过程中原子态的自旋压缩、量子Fisher信息和最大自旋涨落.结果表明:自旋压缩,大于1/2的最大自旋涨落可以作为量子纠缠的充分必要判据.自旋压缩,大于1/2的最大自旋涨落和量子纠缠,它们互相等价.大于1的Fisher信息与它们之间没有等价关系,但可以作为自旋压缩和量子纠缠的充分判据.     

CDn体系DEPT谱线的理论研究

本文根据算符函数的幂级数展开,给出了描述高自旋弱耦合体系的积算符理论,并用来描述I_n S((1)/2)体系(其中I=1/2,1,…)的DEPT实验.给出I(1)_n S((1)/2)体系(例如CD_n)DEPT谱线的增益系数的普遍公式,并提出了用作图法得出谱线结构的方法.     

The Application of Operator Formalism for Describing Experiments in Multipole Spin Systems under Multipulse Actions

An operator formalism is developed which allows multi-pulse actions on scalar-coupled spin systems with quadrupole nuclei to be analyzed. The formulas describing the evolution of angular-momentum operators under the action of a spin-spin interaction Hamiltonian are derived. The calculation of an NMR-spectrum for scalar-coupled multipole spin systems of the AX (A = 1/2, X = 1, 3/2) and AMX (M = 1, X = 1) types is presented and the polarization transfer processes under multi-pulse action are examined as examples of application of the operator formalism. A series of pulse sequences is proposed which allows individual longitudinal spin orders to be observed.     

应用积算符理论研究弱耦合双自旋体系的Raman磁共振谱

从积算符理论和实验上详细地研究了弱耦合双自旋体系（CHCl₃的C-H双自旋体系）的Raman磁共振谱．对不同射频场强度及频偏的Raman谱进行了细致的理论和实验研究，表明积算符理论的计算与实验不仅在弱射频场而且在强射频场时都符合得相当好，克服了微扰论的局限，这为进一步研究复杂自旋体系的Raman谱提供了强有力的理论方法．研究还表明，小的射频频偏将有利于多量子跃迁信号的观测，而适当的射频场强则会提高多量子峰的强度 关键词：     

Fock space for fermion-like lattices and the linear Glauber model

The concept of Fock space representation is developed to deal with stochastic spin lattices written in terms of fermion operators. A density operator is introduced in order to follow in parallel the developments of the case of bosons in the literature. Some general conceptual quantities for spin lattices are then derived, including the notion of generating function and path integral via Grassmann variables. The formalism is used to derive the Liouvillian of the d-dimensional Linear Glauber dynamics in the Fock-space representation. Then the time evolution equations for the magnetization and the two-point correlation function are derived in terms of the number operator.     

On the relativistic spin projection operators

In the Rarita-Schwinger formalism, the relativistic spin projection operators are discussed with the help of the Pauli-Lubanski four-vector. It is shown that this approach is equivalent to the conventional one, but moreover, it enables one to derive recurrence relations for the spin projection operators. Such relations can be useful in practical applications.     

The problem of summation over physical states in a theory of interacting spin waves

A new representation for the spin operators is suggested and on its basis the formalism involving both the rigorousness of diagram technique for the spin operators and the simplicity of diagram technique for the Fermi- and Bose-system is developed to calculate the Green's spin functions. This method is a basis for constructing a theory of high-frequency and thermodynamic properties of the magnetic ordered crystals and a systematic summation over physical states of interacting magnons at any temperatures.     

Superspin in NMR: Application to the ABX system

Superspin is defined to be the angular momentum associated with operators on a nuclear spin system. These operators correspond to magnetizations and the effect of a pulse on these magnetizations is most easily calculated using this formalism. The derivation of the superspin characteristics of the magnetizations in an ABX system is given in detail.     

Product Operator Theory for Spin‐5/2 Nuclei: Application to 2D J‐Resolved NMR Spectroscopy

Product operator theory is a simple quantum mechanical method that has often been used to analytically describe multi‐pulse NMR experiments for weakly coupled spin systems. Considering the existence of 2D‐J resolved NMR spectra of aqueous solutions containing S = 5/2 nuclear spins, the product operator formalism has been extended to the weakly coupled IS (I = 1/2, S = 5/2) spin system. The evolution of I_x, I_y, I_xS_z and I_yS_z product operators under spin–spin coupling Hamiltonian are given here. The analytical results obtained are applied to the well‐known gated decoupler pulse sequence for heteronuclear 2D‐J resolved NMR spectroscopy.     

Quantum cosmology with fermionic matter

The quantum evolution of homogeneous isotropic cosmological models with ferm ionic matter described by spinor fields is investigated within the framework of the formalism of superspace quantization. The fact that quadratic combinations of fermionic operators (current density, spin density, Lagrangian, etc.) are bosonic operators and admit an explicit Schrödinger representation is used in an essential way. It is shown that the DeWitt equation for the cosmological models with fermionic matter under consideration has the form of the Schrödinger equation, so that a correct definition is possible for the probability density of the existence of the models under consideration, in which the singularity is removed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 15–19, March, 1990.