Das Problem der körperfesten Achsen bei Systemen mit gleichen Teilchen

The suitable choice of a body-fixed frame of reference (BFR) is an essential point in the treatment of systems with identical particles. Starting from the fact that there exists a “best” BFR (“specific decoupling”), in which the wave function is a product of an internal and a collective part, we show that the collective term has to be invariant under permutations of the particles. On the other side in symmetrical configurations the BFR has to jump in a well-defined manner under those permutations which are equivalent to spatial rotations. It is shown that for non-symmetrical configurations the BFR must have the same properties. For 3 identical particles it is possible to construct in a purely geometrical way a BFR which has the right behaviour under particle permutations. The Hamiltonian in that BFR is derived and the connection with the “best” BFR is discussed.     

Barriers to internal rotation and tunnelling splittings of the torsional states in the HO(CH2)OH,DO(CH2)OH and DO(CH2)OD molecules

Torsional states caused by vibrations of hydroxyl groups in the methanediol molecule and its two deuterated analogues – DO(CH₂)OH and DO(CH₂)OD were analysed at MP2/cc-pVTZ and CCSD(T)/cc-pVQZ levels of theory. In the first case, 2D PES and 2D surfaces of kinematic coefficients were calculated with geometry optimisation for all other geometric parameters, and in the second case, only the energy of optimised configurations at the MP2/cc-pVTZ level of theory was determined. Then 2D PES was recounted to the complete basis set (CBS) limit by extrapolating the results of calculations at the MP2/cc-pVTZ and MP2/cc-pVQZ levels of theory The calculated values were then averaged over four equivalent points on the coordinate plane. Hamiltonian matrices were constructed using DVR and Fourier methods. After their subsequent diagonalization, the energies of the stationary torsional states were computed. Their classification by C_2V(M) and C_S(M) molecular symmetry groups has been performed. The splitting values due to the tunnelling of the thirty most deeply located torsional states in the three studied molecules were also determined. The torsional states, internal rotation barriers, and tunnelling frequencies in the molecules of methanediol and hydrogen trioxide were compared.     

C42+分子的T  e系统的Jahn-Teller效应与各向异性现象

依据Jahn-Teller效应理论与量子理论,利用群论和对称性分析的方法探讨了具有Td对称性构型的C42+分子的T  e 系统的Jahn-Teller效应与各向异性问题。构建了T  e系统的电声耦合哈密顿量,借助么正平移变换求出了系统的基态与激发态及其能量。结果发现,由于电声耦合作用的缘故,系统发生了Jahn-Teller畸变,畸变导致在系统的势能面上形成了3个具有D2d对称性的势阱。无论系统处在哪一个势阱中,系统原初三重简并的能级都将分裂为两条能级。畸变还导致C42+分子从Td对称性降低到D2d对称性,同时C42+分子的振动频率发生分解,而频率的分解致使C42+分子的各向同性遭到破坏而呈现出各向异性。     

C42+分子的T  e系统的Jahn-Teller效应与各向异性现象

依据Jahn-Teller效应理论与量子理论,利用群论和对称性分析的方法探讨了具有Td对称性构型的C42+分子的T  e 系统的Jahn-Teller效应与各向异性问题。构建了T  e系统的电声耦合哈密顿量,借助么正平移变换求出了系统的基态与激发态及其能量。结果发现,由于电声耦合作用的缘故,系统发生了Jahn-Teller畸变,畸变导致在系统的势能面上形成了3个具有D2d对称性的势阱。无论系统处在哪一个势阱中,系统原初三重简并的能级都将分裂为两条能级。畸变还导致C42+分子从Td对称性降低到D2d对称性,同时C42+分子的振动频率发生分解,而频率的分解致使C42+分子的各向同性遭到破坏而呈现出各向异性。     

Stability of symmetries for equilibrium configurations ofN particles in three dimensions

We consider equilibrium configurations ofn identical particles in three dimensions interacting via two-body potentials depending only on the distance. The symmetry group of a given configuration is defined as the subgroup of isometries which leaves it invariant, up to permutations of the particles. We prove the stability of the symmetry in the following sense: the symmetry group of an equilibrium configuration is the same for the neighboring equilibria arising from any small enough perturbation of the initial potential. Furthermore, for a large class of realistic potentials, the existence of nontrivial symmetries is proved, thus giving a completely geometrical, although partial, approach to the classical crystal problem.     

Symmetry of torsional motion between nonequivalent equilibrium configurations in the CH2DOH molecule

It is shown that the symmetry of torsional motion between energetically nonequivalent equilibrium configurations of the CH₂DOH isotopomer of the methanol molecule can be described by using the dynamic noninvariant group, i.e., a group that is larger than the group of symmetry of the Hamiltonian of intramolecular motion in the Born-Oppenheimer approximation. This allows us to easily determine the nuclear statistical weights of stationary states with allowance for the mixing of nonequivalent configurations and to develop a consistent procedure for purely qualitative construction of the operators of physical quantities describing the torsional-rotational spectrum of this molecule in an arbitrary vibronic state.     

External Electric Field Effect on Hydrogenic Donor Impurity in Zinc-Blende InGaN Quantum Dot

The binding energy of a hydrogenic donor impurity in zinc-blende (ZB) InGaN quantum dot (QD) is calculated in the framework of effective-mass envelope-function theory using the plane wave basis. It is shown that the donor binding energy is highly dependent on the impurity position, QD size and the external electric field. The symmetry of the electron probability distribution is broken and the maximum of the donor binding energy is shifted from the centre of QD in the presence of the external electric field. The degenerating energy levels for symmetrical positions with respect to the centre of QD are split. The splitting increases with the increase of QD height while the splitting increases up to a maximum value and then decreases with the increase of QD radius.     

Primary and secondary isotope effect on tunnelling in malonaldehyde using a quantum mechanical scheme

Primary and secondary isotope effect on tunnelling in malonaldehyde is investigated with reduced-dimensional quantum mechanical models in the saddle-point normal coordinates, where the Hamiltonian takes the imaginary-frequency normal model as the reaction coordinate and uses the relaxed potentials to approximate the normal modes not explicitly included. Our two-dimensional (2D) results of the ground-state tunnelling splitting (Δ₀), as well as the ratio of the Δ₀ in malonaldehyde to that in its isotopologues, are in reasonably good agreement with available experimental data. The experimental deduction about the appreciable impact of secondary isotope effect on tunnelling is further confirmed. Moreover, we find that in most isotopologues, the fundamental excitation of the ring-deformation normal mode, explicitly included in the 2D model, shows a large enhancement of tunnelling relative to the Δ₀.     

Quantum mechanical solution to spectral lineshape in strongly-coupled atom-nanocavity system

The strongly coupled system composed of atoms, molecules, molecule aggregates, and semiconductor quantum dots embedded within an optical microcavity/nanocavity with high quality factor and/or low modal volume has become an excellent platform to study cavity quantum electrodynamics (CQED), where a prominent quantum effect called Rabi splitting can occur due to strong interaction of cavity-mode single-photon with the two-level atomic states. In this paper, we build a new quantum model that can describe the optical response of the strongly-coupled system under the action of an external probing light and the spectral lineshape. We take the Hamiltonian for the strongly-coupled photon-atom system as the unperturbed Hamiltonian $\bm{H}$₀ and the interaction Hamiltonian of the probe light upon the coupled-system quantum states as the perturbed Hamiltonian $\bm{V}$. The theory yields a double Lorentzian lineshape for the permittivity function, which agrees well with experimental observation of Rabi splitting in terms of spectral splitting. This quantum theory will pave the way to construct a complete understanding for the microscopic strongly-coupled system that will become an important element for quantum information processing, nano-optical integrated circuits, and polariton chemistry.     

The action of transformations of the point group of a molecule on its instantaneous nuclear configuration

The action of the transformations of a point group of a rigid molecule in a specified electronic state on the instantaneous nuclear configuration of the molecule is considered. This action is shown to be equivalent to permutations of identical nuclei in the effective potential of interaction of the nuclei in this state, which is invariant with respect to the transformations of the point group. Therefore, the point group characterizing the electronic state should be used as the rigorous symmetry group of the total electronic-vibrational-rotational motion.     

Spin tunnelling in mesoscopic systems

We study spin tunnelling in molecular magnets as an instance of a mesoscopic phenomenon, with special emphasis on the molecule Fe₈. We show that the tunnel splitting between various pairs of Zeeman levels in this molecule oscillates as a function of applied magnetic field, vanishing completely at special points in the space of magnetic fields, known as diabolical points. This phenomena is explained in terms of two approaches, one based on spin-coherent-state path integrals, and the other on a generalization of the phase integral (or WKB) method to difference equations. Explicit formulas for the diabolical points are obtained for a model Hamiltonian.     

The isometric group of non-rigid molecules

A new method for derivation of symmetry groups of non-rigid molecules is presented, based on the concept of isometry of nuclear configurations defined by a certain number of internal (structural) coordinates. The substitution group of the internal coordinates interrelating isometric nuclear configurations generates the internal isometric group by both permutations and intransitive imprimitive substitution groups, and together with the covering group it generates the full isometric group. Examples for these groups are given. It is shown that the rotation-internal motion hamiltonian is symmetric with respect to the isometric group. The relation between various approaches to the isometric group is investigated; the role of automorphisms is pointed out. The new approach is shown to give a self-consistent procedure for the quantum mechanical problem associated with the rotation-internal motion hamiltonian.     

Permutation-inversion symmetry of C70 fullerite in the high-temperature phase

The permutation-inversion symmetry group of C₇₀ fullerite in its high-temperature phase is constructed with allowance for the rotation of its constituent molecules, and the local symmetry group of a rotating molecule in the crystal is identified. Irreducible representations of these groups are constructed that are compatible with the principle of wave-function symmetry with respect to permutations of identical nuclei. A group-theoretic classification is made of the quantum states of a rotating molecule and of the crystal in the high-temperature phase of C₇₀ fullerite. Selection rules are derived for electronic, vibrational, and rotational spectra in terms of irreducible representations of the permutation-inversion symmetry group of the crystal. Fiz. Tverd. Tela (St. Petersburg) 39, 1895–1901 (October 1997)     

自旋对磁量子反点能谱和磁电导的影响

利用分区求解单粒子薛定谔方程的方法,研究了电子自旋对磁量子反点中电子能级和磁电导的影响.结果表明,电子自旋与非均匀磁场的相互作用使电子能级发生劈裂,其特征与均匀磁场中电子自旋引起的劈裂显著不同,磁量子反点中能级的劈裂与角动量量子数密切相关.电子共振隧穿到磁边缘态,导致了磁电导随磁场的非周期性振荡.考虑电子自旋与不考虑电子自旋相比,磁电导谱中谷的数目增多且深度减小. 关键词：     

半导体缺陷能级的应力效应

本文讨论用瞬态方法测量立方半导体缺陷能级应力移动和判别缺陷势对称性的有关问题。对于简并能级E_s引入应力下分裂平均值E_s,它具有原哈密顿群对称操作不变性,因此可以用群论方法得出应力系数间关系并用以判断缺陷势对称性。比如当缺陷势具有T群以上对称时,缺陷能级平均值E_T相对导带底或价带顶单轴应力系数(?(E_c-E_T))/(?F)或(?(E_T-E_v))/(?F)与应力F方向无关且等于流体静压系数的1/3。也讨论了C_3v对称缺陷势的情况。缺陷能级对导带的平均电子发射率e_n和俘获率c_n满足简洁关系 e_n=g_Tg_c^-1c_nN′_ce^{(-(E_c-E_T)/kT)}。指出通过测量e_n的应力关系判断缺陷势对称性的各种方案比较。分析了用瞬态法测量e_n有关问题。当E_T分裂但诸能级间允许跃迁时,瞬态讯号呈单指数衰减,时间常数为e_n^-1。当E_T分裂但诸能级间禁止跃迁时,瞬态讯号呈多指数衰减。用初始斜率可求得e_n。 关键词：     

Dephasing of quantum tunnelling in molecular nanomagnets

Dephasing mechanism of quantum tunnelling in molecular magnets has been studied by means of the spin-coherentstate path integral in a mean field approximation. It is found that the fluctuating uncompensated transverse field from the dipolar-dipolar interaction between molecular magnets contributes a random phase to the quantum interference phase. The resulting transition rate is determined by the average tunnel splitting over the random phase. Such a dephasing process leads to the suppression of quenching due to the quantum phase interference, and to the steps due to odd resonances in hysteresis loop survived, which is in good agreement with experimental observations in molecular nanomagnets Fes and Mn12.     

Problem of mixing of stereoisomers in the hydrazine molecule N2H4

It is shown that the important consequence of nonrigid motions observed in the hydrazine molecule N₂H₄ is mixing of stereoisomers, although the geometrical symmetry group, taking into account these motions, similarly to the point group of one equilibrium configuration, has no improper transformations of the molecule as a whole. Here, an important point is that the geometrical group of a nonrigid molecule is the so-called noninvariance dynamical group. The effect of mixing of stereoisomers on the total picture of nonrigid motions is considered using the symmetry methods. In particular, it is shown that a nonrigid molecule exhibits properties of a symmetric top, whereas a rigid molecule represents an asymmetric top.     

Kondo quantum criticality of magnetic adatoms in graphene

We examine the exchange Hamiltonian for magnetic adatoms in graphene with localized inner shell states. On symmetry grounds, we predict the existence of a class of orbitals that lead to a distinct class of quantum critical points in graphene, where the Kondo temperature scales as TK∝|J-Jc|1/3 near the critical coupling Jc, and the local spin is effectively screened by a super-Ohmic bath. For this class, the RKKY interaction decays spatially with a fast power law ～1/R7. Away from half filling, we show that the exchange coupling in graphene can be controlled across the quantum critical region by gating. We propose that the vicinity of the Kondo quantum critical point can be directly accessed with scanning tunneling probes and gating.     

Spin-related phenomena in InAs/GaSb quantum wells

We have studied theoretically the influence of symmetry breaking mechanisms: structural inversion asymmetry, bulk inversion asymmetry, relativistic and non-relativistic interface Hamiltonian and warping on spin split of levels ΔE and optical absorption of linearly polarized light in asymmetrical quantum wells made from zincblende materials grown on [001] direction. The AlSb/InAs/GaSb/AlSb broken-gap quantum wells with hybridized electron-hole states sandwiched by the AlSb barriers have been considered. We have obtained substantial contributions of these effects into the absolute values of spin split of electron and hole states and spinflip optical transitions for the initial state in-plane wave vectors along low symmetry directions such as [12].     

Resonant tunneling of a few-body cluster through repulsive barriers

A model for quantum tunnelling of a cluster comprised of A identical particles, interacting via oscillator-type potential, through short-range repulsive barrier potentials is introduced for the first time in symmetrized-coordinate representation and numerically studied in the s-wave approximation. A constructive method for symmetrizing or antisymmetrizing the (A ? 1)-dimensional harmonic oscillator basis functions in the new symmetrized coordinates with respect to permutations of coordinates of A identical particles is described. The effect of quantum transparency, manifesting itself in nonmonotonic resonance-type dependence of the transmission coefficient upon the energy of the particles, their number A = 2, 3, 4 and the type of their symmetry, is analyzed. It is shown that the total transmission coefficient demonstrates the resonance behavior due to the existence of barrier quasi-stationary states, embedded in the continuum.