异核偶极相互作用非久期项对交叉极化弛豫速率的影响

本文通过计入异核偶极相互作用的非久期项对交叉极化弛豫速率的影响而推广交叉极化理论。自旋系统内部的快运动可以使得异核偶极相互作用的非久期项对交叉弛豫的贡献变得可观。本文给出了交叉弛豫速率的一般公式,并讨论了本理论在交叉极化实验中的应用。     

固体高分辨NMR中的DANTE实验

该文给出了旋转固体的DANTE实验的严格的理论分析,在化学位移相互作用坐标系中,应用平均Hamiltonian理论求出了自旋体系运动方程的零级近似解,从而讨论了DANTE序列在不同情况下的选择性,并给出了有关的实验结果.     

Tavis-Cummings模型中原子间偶极相互作用对场熵演化特性的影响

研究了单模辐射场与耦合双原子相互作用系统场熵的演化特性,讨论了原子间偶极相互作用对场熵演化特性的影响.研究结果表明,当原子间偶极偶极相互作用不太强时,场熵的时间演化行为与单光子JC模型相似;当原子间偶极偶极相互作用足够强时,场熵的时间演化行为与双光子JC模型相似 关键词： 单模辐射场 耦合双原子 场熵演化     

压缩真空场与耦合双原子Raman相互作用系统场熵的演化特性

利用全量子理论,研究了压缩真空场与耦合双原子Raman相互作用系统的场熵演化特性,讨论了系统耦合常数和光场初始压缩因子对场熵演化特性的影响.结果表明,场熵的时间演化规律与原子布居差的时间演化规律非常相似.当原子间的偶极-偶极相互作用较弱时,场熵演化呈现周期性的崩塌与回复现象;当原子间的偶极-偶极相互作用较强时,场熵演化呈现不规则振荡,崩塌与回复周期现象消失.     

两个原子与双模腔场的多光子相互作用：场和原子的动力学性质

研究一对偶极相互作用原子与双模量子腔场的多光子相互作用，分析场和原子的动力学性质，给出腔模平均光子数和原子反转度时间演化的解析表达式，考察腔模初态、初场强度以及原子间偶极－偶极相互作用的影响。     

耦合双原子与非线性相干态相互作用模型的腔场谱

研究了两个偶极 偶极相互作用的全同二能级原子与高Q腔内非线性相干态光场相互作用过程的腔场谱 .讨论了原子间耦合强度、初始场光子数分布和初始场强度的改变对光谱结构的影响.     

两个双能级原子与双模腔场的拉曼相互作用

研究了两个双能级原子与双模辐射腔场的拉曼相互作用，计算了两个原子与腔场具有相同耦合常数但同时考虑原子间偶极一偶极相互作用情形下的辐射谱．讨论了双模腔场处于不同数态时辐射谱的新特点．     

魔角旋转核磁共振波谱学

样品绕与外加恒定磁场方向成魔角β_M=cos^-1(1)/√3的轴向快速旋转(MAS)可以消除固体NMR的多种谱增宽。本文首先介绍了固体中的几种主要的各向异性相互作用,即偶极-偶极,核四极,自旋-自旋或称间接偶极-偶极以及化学位移相互作用。然后用平均哈密顿理论阐述了MAS对这些相互作用的影响。现今的固体高分辨方法有四种,即多脉冲(MP),多量子(MQ),交叉极化和大功率异核去耦合(CP)以及MAS,在这些方法中MAS方法是唯一可以获得各向同性化学位移的。因而要得到类似于液体谱的固体高分辨,MAS往往是最后的手段。以上这些方法的联合运用以及极为广泛的应用研究使得固体高分辨NMR兴旺发达起来了。本文引述了大量原始和最新的文献,力图概述当前该领域中的大部分成就。评论这一领域的理论和实验技术的发展。     

两个能级原子与双模腔场的拉曼相互作用

研究了两个双能有原子与双模辐射腔场的拉曼相互作用，计算了两个原子与腔场具有相同耦合常数但同时考虑原子间偶极－偶极相互作用情形下的辐射谱，讨论了双模腔场下于不同数态时辐射新特点。     

两个原子与双模腔场多光子相互作用过程中光场的相位性质

研究了偶极－偶极关联的两个全同二能级原子与双模强相干光场多光子共振相互作用过程中光场相位的演化性质,分别讨论了三种不同原子初态下,初态场强度和原子间偶极相互作用对光场相位概率分布,相位扩散及频率漂移的影响。     

Theoretical investigations of the vapour-liquid equilibrium and dielectric properties of dipolar Yukawa fluids in an external field

In a low field approximation, using the dipolar Yukawa fluid model (in mean spherical approximation as a reference system) a consistent field-dependent free energy expression is proposed for the calculation of the vapour-liquid equilibrium of polar fluids in an applied electric field. A perturbation theory high field approximation expression of the free energy is also proposed to study the field-dependent properties of fluids. In the high field approximation, equations for the field-dependent polarization and for the nonlinear dielectric constant (or Piekara constant) are also predicted. It has been discussed that our approximations are appropriate to describe the vapour-liquid-like phase equilibria and the magnetization curves of magnetic fluids.     

Evolution of solid state systems containing mutually coupled dipolar and quadrupole spins: perturbation treatment

Perturbation approach to time evolution of multi-spin systems containing quadrupole and dipolar spins has been presented and discussed. The treatment comprises polarization transfer effects, field-dependent relaxation processes of dipolar as well as quadrupole spins and combined results of both of them. Complete theories dealing with various aspects of the spin dynamic processes have been proposed. Because of an educational character of this paper, relevant assumptions, limitations and even particular steps of the proposed treatments have been discussed in detail. Special emphasis is put on understanding of validity regimes of the perturbation treatment, depending on relative strengths of spin interactions and timescales of relevant motional processes affecting them. Motional regimes required for spins to be involved in essentially different evolution pathways like polarization transfers or relaxation have been illustrated by experimental examples.     

Distortions in multiple-pulse solid state NMR imaging: gradient decoupling, time-sequenced second averaging, and over-sampling

Three approaches to reducing image artifacts are described that are specific to multiple-pulse line-narrowing methods of NMR imaging. Gradient decoupling avoids excess line broadening from off-resonance gradient phase evolution by restricting the gradient to selected windows in which the gradient Hamiltonian commutes with the toggling frame state, and where the averaged Hamiltonian between gradient pulses is either cyclic or anti-cyclic. This forces the residual averaged dipolar Hamiltonian to be independent of the gradient evolution. Time-sequenced second averaging addresses the on-resonance broadening, where residual error terms dominate the spin dynamics (a lack of second averaging), by adding a second coherent averaging that retains part of the modulation associated with off-resonance terms, and thus smoothes out the line-narrowing efficiency with spatial offset. Over-sampling is useful to increase both the resolution and sensitivity of an image, but it introduces a sampling modulation that produces sidebands. These are eliminated by a series of prepulses in a fashion reminiscent of CYCLOPS phase cycling.     

Canonical transformation approach to the intermediate-coupling T-t Jahn-Teller effect

A canonical transformation is proposed to handle the T-t dynamical Jahn-Teller problem. The coupling term of the transformed Hamiltonian is treated as a small perturbation. The vibronic energy lowering for the ground state of the system is evaluated and compared with the exact numerical calculation of Cancer and Englman.¹ It is shown that the second-order perturbation theory gives accurate results in the weak- and intermediate-coupling regions.     

Cotunneling through a quantum dot coupled to ferromagnetic leads with noncollinear magnetizations

Spin-dependent electronic transport through a quantum dot has been analyzed theoretically in the cotunneling regime by means of the second-order perturbation theory. The system is described by the impurity Anderson Hamiltonian with arbitrary Coulomb correlation parameter U. It is assumed that the dot level is intrinsically spin-split due to an effective molecular field exerted by a magnetic substrate. The dot is coupled to two ferromagnetic leads whose magnetic moments are noncollinear. The angular dependence of electric current, tunnel magnetoresistance, and differential conductance are presented and discussed. The evolution of a cotunneling gap with the angle between magnetic moments and with the splitting of the dot level is also demonstrated.     

VPT2+K spectroscopic constants and matrix elements of the transformed vibrational Hamiltonian of a polyatomic molecule with resonances using Van Vleck perturbation theory

Vibrational levels of polyatomic molecules are analysed with Van Vleck perturbation theory to connect experimental energy levels to computed molecular potential energy surfaces. Vibrational matrix elements are calculated from a quartic potential function via second-order Van Vleck perturbation theory, a procedure that treats both weak and strong interactions among vibrational states by approximately block-diagonalising the vibrational Hamiltonian. A clear and complete derivation of anharmonic and resonance constants as well as general expressions for both on- and off-diagonal matrix elements of the transformed Hamiltonian is presented. The equations are written in partial fraction form and as a constant multiplied by a harmonic oscillator matrix element to facilitate removing the effect of strongly interacting resonant states both in analytical formulae and in computer code. The derived equations are validated numerically, and results for the isotopomers of formaldehyde (H₂CO, HDCO, D₂CO) are included. The implications of the equations on zero-point energy calculations and experimental fits are discussed. The VPT2+K method is defined by these results for use in fitting and calculating vibrational energy levels.     

Higher-order calculations in the real space dynamic renormalization group: One dimension

The application of real space dynamic renormalization group methods to the one-dimensional kinetic Ising model, discussed in an earlier paper, is extended to one order higher in perturbation theory than was done previously. It is shown that the treatment of short-range, local quantities is improved in going to higher order in the perturbation expansion, while that of the long-range properties remains largely unaffected. Arbitrariness in the real space mapping function and how it may be exploited to our advantage is duscussed. It is shown that the renormalized Hamiltonian continues to be characterized by one coupling through second order. We find that the single spin-flip kinetic Ising model generates at second-order new spin-flip mechanisms in the renormalized dynamical operator but that their effects are small (at most 2%) over the entire temperature range.     

Secondary resonances in Penning traps. Non-lie symmetry algebras and quantum states

The Penning trap Hamiltonian (hyperbolic oscillator in a homogeneous magnetic field) is considered in the basic three-frequency resonance regime. We describe its non-Lie algebra of symmetries. By perturbing the homogeneous magnetic field, we discover that, for special directions of the perturbation, a secondary hyperbolic resonance appears in the trap. For corresponding secondary resonance algebra, we describe its non-Lie permutation relations and irreducible representations realized by ordinary differential operators. Under an additional (Ioffe) inhomogeneous perturbation of the magnetic field, we derive an effective Hamiltonian over the secondary symmetry algebra. In an irreducible representation, this Hamiltonian is a model second-order differential operator. The spectral asymptotics is derived, and an integral formula for the asymptotic eigenstates of the entire perturbed trap Hamiltonian is obtained via coherent states of the secondary symmetry algebra.     

A Direct Calculation of First-Order Wave Function of Helium

We develop a simple analytic calculation for the first order wave function of helium in a model in which nuclear charge screening is caused by repulsive coulomb interaction. The perturbation term, first-order correlation energy, and first-order wave function are divided into two components, one componentassociated with the repulsive coulomb interaction and the other proportional to magnetic shielding. The resulting first-order wave functions are applied to calculate second-order energies within the model. We find that the second-order energies are independent of the nuclear charge screening constant in the unperturbed Hamiltonian with a central coulomb potential.     

The low-temperature 13C and 2H spectra and relaxation rates of methyl groups depend on the azimuth of B0 in the molecular frame. Those of 1H do not. Why?

It is shown that the answer to the question asked in the title is: Because the axial symmetry axes of the H-H dipolar coupling tensors in a -CH3 group are perpendicular to the (assumed) threefold axis of the group. By contrast, those of the 13C-H dipolar and 2H quadrupolar coupling tensors are not. The use of "symmetry adapted" spin functions and of a symmetry adapted form of the (dipolar) coupling Hamiltonian greatly simplifies the analysis.