基于臭氧分子体系的动力学研究

在李代数动力学群得到Hamiltonian的基础上,通过求解正则运动方程.对固定键角近似下臭氧分子体系相空间的庞加莱截面、KAM环面以及振动体系的能量属性进行了研究,获得了有关臭氧分子振动体系丰富的动力学信息.     

动力学对称群方法对三原子分子高激发振动态的理论研究

利用动力学对称群方法研究了弯曲三原子分子的振动高激发态能谱-该方法显示：三原子分子的动力学对称性为U₁(4)U₂(4),则三原子分子的Hamiltonian量可写成代数的各元素之和,通过李代数处理而求得分子代数Hamiltonian量的本征值,进而得到分子的振动能谱-并具体计算了O₃分子- 关键词：     

红外场对双原子分子振动布居影响的李代数方法研究

采用李代数方法研究双原子分子在红外场中的振动跃迁,给出了体系跃迁概率的解析表达,并讨论了红外场的频率、光强和脉冲持续时间分别对NaCl和LiH分子振动基态和第一振动激发态上粒子数布居的影响. 关键词： 李代数方法 红外场 振动布居 双原子分子     

用李代数方法构造四原子分子的势能面

把李代数方法得到的四原子分子的代数Hamiltonian，利用相干态经典化之后并找到一个新的变换，将分子的键角引入，而得到四原子分子的势能面.由该势能面计算得到的解离能与力常数与其他方法给出的一致.     

线性三原子分子转动-振动能谱的李群处理方法

本文利用李代数方法与二次量子化理论计算了线性三原子分子的转动-振动能谱.结果表明,如果将分子的转动与振动均看作是谐振子,则可以导致这种分子的转动-振动能谱公式.     

S2O激发态(C1A'')振动光谱及势能面的一种代数研究

利用代数方法研究了非对称弯曲三原子分子S2O分子处于C1A'电子态的能谱及其稳定构型下的势能面,通过对30条光谱数据的拟和得到的rms误差为2.40 cm-1.结果表明,利用此代数Hamiltonian很好的实现了能级再现,它预测了振动总量子数达到20的全部振动能级,同时我们计算了分子的解离能与力常数.通过与实验值比较证明了这种方法在计算这类分子的有效性.     

S_2O激发态(~1A′)振动光谱及势能面的一种代数研究(英文)

利用代数方法研究了非对称弯曲三原子分子S_2O分子处于(?)~1A′电子态的能谱及其稳定构型下的势能面,通过对30条光谱数据的拟和得到的rms误差为2.40 cm~(-1)。结果表明,利用此代数Hamiltonian很好的实现了能级再现,它预测了振动总量子数达到20的全部振动能级,同时我们计算了分子的解离能与力常数。通过与实验值比较证明了这种方法在计算这类分子的有效性。     

Loop代数L(D_r)上的推广Toda力学系统研究

对Loop代数L(Dr)上具有长程相互作用的Toda力学系统进行推广 ,用一组有序整数对 (X ,Y)来表示Toda链 ,构造出Loop代数L (Dr)的LaxPair,并给出了系统在 (3,2 )Toda链情况下的运动方程和Hamiltonian结构 .在此模型中 ,标准的Toda变量之间和附加的坐标变量之间的泊松括号都非零 ,部分附加的坐标变量之间的泊松结构构成李代数 .     

S2O分子高激发振动光谱及势能面的代数研究

本文利用代数方法研究了非对称弯曲三原子分子S2O分子处于C～1A′电子态的能谱及其稳定构型下的势能面,通过对30条光谱数据的拟和得到的RMS误差为2.40 cm-1.结果表明,利用此代数Hamiltonian很好的实现了能级再现,它预测了振动总量子数达到20的全部振动能级(在本文中我们只列举到v= 9),同时我们计算了分子的解离能与力常数.通过与实验值比较证明了这种方法在计算这类分子的有效性.     

分子高激发振动态的理论研究

简要综述了分子高激发振动态的理论研究方法和研究进展.介绍了李代数方法在高激发振动态能级的归属和分类、分子高激发振动态动力学以及分子内振动能量弛豫和分子解离等方面的应用.随后,作者对分子高激发振动态研究领域今后的发展方向作了展望.     

Influence of soliton distributions on the spin-dependent electronic transport through polyacetylene molecule

In this paper, a detailed numerical study of the role of selected soliton distributions on the spin-dependent transport through trans-polyacetylene (PA) molecule is presented. The molecule is attached symmetrically to magnetic semi-infinite three-dimensional electrodes. Based on Su– Schrieffer–Heeger (SSH) Hamiltonian and using a generalized Green’s function formalism, we calculate the spin-dependent currents, the electronic transmission and tunnelling magnetoresistance (TMR). We found that the presence of a uniform distribution of the soliton centres along the molecular chain reduced the size of the band gap of trans-PA molecule. Moreover, a sublattice of the correlated solitons as binary clusters, which are randomly distributed along the chain, can induce extended electronic states in the band gap of the molecule. In this case, the band gap of the molecule is suppressed and at lower voltages, the TMR bandwidth is narrowed. The current–voltage characteristic then shows an ohmic-like behaviour.     

A symmetry-based approach to the effective Hamiltonian for symmetric top molecules in degenerate vibronic states

The effective Hamiltonian for a symmetric top molecule in a degenerate vibronic state is obtained. Included in this Hamiltonian are the rotational, spin-rotational, spin-orbit coupling and electronic spin-spin interactions. The terms of the Hamiltonian are expressed as the product of molecular ‘constants,’ rotational angular momentum operators, and symmetry operators. A formalism is derived, and tables included, to determine whether or not a symmetry operator vanishes for a given vibronic state of a particular molecular symmetry. In this way, one can easily obtain all the non-vanishing Hamiltonian terms for a particular application.     

用于测量J偶合常数的同时多层选择性恒时J分解谱的方法

标量偶合是核磁共振（NMR）波谱的一个重要参数.其中氢-氢偶合能提供关于分子结构的有用信息.但是,在复杂的偶合网络中解析出氢-氢偶合常数（J_H-H）较为困难.本文提出了一种基于空间编码选择性恒时演化的测量J_H-H的方法,利用一次实验就能解析分子中所有氢核的偶合网络,并测量J_H-H.该方法被称为同时多层选择性恒时J分解谱（SMS-SECTJRES）.它结合空间编码梯度和选择性恒时演化,并利用平面回波谱成像（EPSI）采样模块,从不同的空间位置提取出对应不同氢核偶合网络的J分解谱,促进了NMR技术在分子结构解析中的进一步应用.     

Driven dissipative dynamics and topology of quantum impurity systems

In this review, we provide an introduction to and an overview of some more recent advances in real-time dynamics of quantum impurity models and their realizations in quantum devices. We focus on the Ohmic spin–boson and related models, which describe a single spin-1/2 coupled with an infinite collection of harmonic oscillators. The topics are largely drawn from our efforts over the past years, but we also present a few novel results. In the first part of this review, we begin with a pedagogical introduction to the real-time dynamics of a dissipative spin at both high and low temperatures. We then focus on the driven dynamics in the quantum regime beyond the limit of weak spin–bath coupling. In these situations, the non-perturbative stochastic Schrödinger equation method is ideally suited to numerically obtain the spin dynamics as it can incorporate bias fields $h_z(t)$ of arbitrary time-dependence in the Hamiltonian. We present different recent applications of this method: (i) how topological properties of the spin such as the Berry curvature and the Chern number can be measured dynamically, and how dissipation affects the topology and the measurement protocol, (ii) how quantum spin chains can experience synchronization dynamics via coupling with a common bath. In the second part of this review, we discuss quantum engineering of spin–boson and related models in circuit quantum electrodynamics (cQED), quantum electrical circuits, and cold-atoms architectures. In different realizations, the Ohmic environment can be represented by a long (microwave) transmission line, a Luttinger liquid, a one-dimensional Bose–Einstein condensate or a chain of superconducting Josephson junctions. We show that the quantum impurity can be used as a quantum sensor to detect properties of a bath at minimal coupling, and how dissipative spin dynamics can lead to new insight in the Mott–superfluid transition.     

线型分子的电子能级之Λ分裂的新解释

认为电子态能级发生Λ分裂虽然是角动量引起的,但不是耦合而是运动牵连作用的结果.从这一认识出发,利用欧拉方程和拉格朗日方程分别得到了包含Λ分裂的分子转动哈密顿函数和哈密顿算符,所得结果与Van.Vleck的著名结论完全一致 关键词： Λ分裂 线型分子 欧拉方程 哈密顿算符     

Charge transfer excitons: dynamic theory of vibronic spectra

The vibronic spectra of charge transfer excitons (CTE) in a molecular one-component or alternatingly ordered two-component chain are treated in the framework of a dynamic approach (neglecting thermal excitations of the intramolecular vibrations). The model introduces two mechanisms of coupling between CTEs and vibrational quanta: (1) shift of the equilibrium positions of the nuclei in the ionized donor or acceptor; (2) change of the vibrational frequency in the ionized molecule. This model allows to generalize the simple CTE Hamiltonian and the vibronic Hamiltonian of Frenkel excitons. The linear optical susceptibility is calculated in the vibronic region (one CTE and one vibrational quantum). The double splitting of vibronics of CTEs was analyzed: (1) the splitting connected with the location of the intramolecular vibration on the donors or on the acceptors; (2) the splitting connected with the symmetry of the vibronic spectra (in the degenerate case). The general structure of the vibronic spectra of CTEs is established. It contains structureless absorption lines, which correspond to two-particle bands (the phonon is excited on a neutral molecule neighboring the donor or the acceptor) and Lorentz-type lines of one-particle states, which correspond to the bound propagation of the CTE and the phonon.     

Infrared spectroscopy of CO on NaCl(100) IV. Bandshape analysis

The infrared bandshape of monolayer CO on NaCl(100) at 4 K is slightly asymmetric and its bandwidth of 0.09 cm⁻¹ is the narrowest observed for any surface molecule. From a variety of experiments we know that this band profile is determined by heterogeneous rather than homogeneous broadening. We offer an explanation for the experimentally observed bandshape by proposing that irregularities in the surface of the cleaved NaCl crystals give rise to many distinct two-dimensional domains of physisorbed CO. A first-order perturbation calculation, which generates the infrared cross-section as a function of domain size, has been used to estimate that on the order of 10⁵ molecules reside in an average size domain. The accuracy of the calculation, whose Hamiltonian represents the intermolecular potential among CO molecules by electric multipole coupling, will be discussed. We use the same coupling Hamiltonian to explore the effect of submonolayer coverages, isotopic dilution, and surface heterogeneities on the infrared spectroscopy of CO on NaCl(100). Our calculations can account for some, but not all, of the observed spectroscopic data.     

Exact Solvability and Quantum Integrability of a Derivative Nonlinear Schrödinger Model

Using a variant of quantum inverse scattering method (QISM) which is directly applicable to field theoretical systems, we derive all possible commutation relations among the operator valued elements of the monodromy matrix associated with an integrable derivative nonlinear Schrödinger (DNLS) model. From these commutation relations we obtain the exact Bethe eigenstates for the quantum conserved quantities of DNLS model. We also explicitly construct the first few quantum conserved quantities including the Hamiltonian in terms of the basic field operators of this model. It turns out that this quantum Hamiltonian has a new kind of coupling constant which is quite different from the classical one. This fact allows us to apply QISM to generate the spectrum of quantum DNLS Hamiltonian for the full range of its coupling constant.     

Theoretical investigations on the orientational dependence of electron transport through porphyrin molecular wire

The effect of molecular orientation on the electron transport behavior of single porphyrin sandwiched between two gold (111) electrodes is investigated by density functional theory calculations combined with non-equilibrium Green’s function method. The results show that the porphyrin with parallel connection to gold (111) electrodes is more conductive than the porphyrin with diagonal connection to gold (111) electrodes. The mechanism of the difference of electron transport for these two molecular junctions is analyzed from the transmission spectra and the molecular projected self-consistent Hamiltonian states. It is found that the intrinsic nature of the molecule, such as the π-conjugated framework and the strength of molecule–electrode coupling, are the essential reason for generating this difference of electron transport for the two molecular systems.     

Hamiltonian,symmetry group,and vibrational coordinates for the nonrigid molecule CXY2CCCXY2

A vibration-torsion-rotation Hamiltonian is derived for a molecule of the type CXY₂CCCXY₂ exhibiting nearly free internal rotation. The Hamiltonian obtained preserves many of the features of the ordinary Wilson-Howard vibration-rotation Hamiltonian and is based qualitatively on the idea of a slowly varying torsional reference configuration from which the atoms make rapid vibrational displacements. The appropriate molecular symmetry group for this molecule is found to be a double group of the simple Longuet-Higgins permutation-inversion symmetry group. The indeterminacy of symmetry species (single-valued vs double-valued) for coordinates used to describe the small amplitude vibrations is illustrated and clarified using a simple model for the skeletal bending vibrations.