Magnetic transitions in strong coupling expansions for nearly degenerate states

A strong coupling expansion for a two‐band Hubbard model on two sites with nearly degenerate states is considered. A comparative analysis is performed for different schemes of perturbation theory which are applicable to systems with nearly degenerate states. A fourth order approach which builds on a four‐dimensional low‐energy subspace with nearly degenerate states captures accurately the transition from an antiferromagnetic to a ferromagnetic ground state at large on‐site Coulomb interaction.     

Correlation energy in a transition metal

Correlation energies of the nondegenerate and the degenerate Hubbard models are calculated with second order perturbation theory and with a variational local ansatz. By comparing these results, we discover an overestimate of the correlation energy in the perturbation treatment. The overestimate is due to the independent treatment of electron correlations in different orbital states. We also demonstrate the qualitative difference in electron correlation between the two models.     

Field form of perturbation theory for calculating the matrix elements of operators between the states of two degenerate atomic levels. I

It is shown that the calculation of the matrix elements between degenerate states of arbitrary atomicmolecular systems can be reduced to a calculation of the matrix elements for some auxiliary operator. The perturbation theory for this calculation can be given a field form, and its matrix elements can be expressed in terms of the contributions from special Feynman diagrams. The exact rules are formulated for constructing the contributions from these diagrams.     

Effects of an electric field on the confined hydrogen impurity states in a spherical parabolic quantum dot

In this paper, we studied the effects of an electric field on a hydrogenic impurity confined in a spherical parabolic quantum dot using nondegenerate and degenerate perturbation methods. The binding energies of the ground and three low-excited states are calculated as a function of the confinement strength and as a function of the intensity of an applied electric field. Moreover, we computed the oscillator strength and the second-order nonlinear optical rectification coefficient based on the computed energies and wave functions. The results show that the electric and optical properties of hydrogenic impurity states are strongly affected by the confinement strength and the applied electric field.     

Radiative properties of diamagnetic levels in atoms: Dependence of transition probability on magnetic field strength

We study the effect of diamagnetic interaction on the probability of radiative transitions of an atom from states split by a field. We write the analytic expressions for the diamagnetic corrections to the matrix elements of transitions belonging to the Lyman and Balmer series and of transitions between arbitrary nondegenerate states in hydrogen. We also discuss the perturbation theory for transitions from degenerate diamagnetic states. The theory is based on expanding in powers of the field strength the eigenfunctions and eigenvalues of the matrix of diamagnetic interaction in the subspace of states with given principal and magnetic quantum numbers. The field changes the coefficients in both the superposition and the degenerate basis. To derive the analytic expressions for the higher-order matrix elements, we use the Sturm expansion of the reduced Coulomb Green’s function. We also elaborate on the features of the frequency dependence of the corrections to the radiative matrix elements, which correlate with the structure of the diamagnetic spectrum of excited levels. Finally, we establish that the magnetic field acts selectively on the diamagnetic components of emission lines: as the field strength increases, an increase in the intensity of certain lines is accompanied by a decrease in the intensity of the other lines. Zh. éksp. Teor. Fiz. 116, 1161–1183 (October 1999)     

The quantum theory of an ideal superlattice responding to far-infrared laser radiation

Minibands of quasienergies can be defined for a superlattice interacting with far-infrared laser radiation. It is demonstrated that the width of these quasienergy minibands depends not only on the parameters of the superlattice, but also on strength and frequency of the driving laser field. In particular, the width approaches zero at certain values of these parameters. A strong coupling ansatz, combined with perturbation theory for degenerate quasienergy states, leads to a detailed understanding of these results.     

Spectrum and Binding Energy of an Off-Center Hydrogenic Donor in aSpherical Quantum Dot

Off-center impurity effects in a spherical quantum dot are theoretically studied by degenerate perturbation method in strong confinement. The energy levels and binding energies are computed for the typical GaAs material as function of the donor position. The numerical results show the quantum size effect. We note that the energy levels and binding energies are not onlyrelated to the position of donor and the strength of confinement,but also related to the fold of degenerate states. We can see obviously that gaps will appear among the degenerate states and the splitting of energy levels and binding energies will appear as the position of the impurity is shifted away off the center.     

Magneto-reflectance of the 1S exciton ground states in InP and GaAs

The reflectance due to the 1S exciton of InP and GaAs is studied in magnetic fields up to 12 T in the Faraday and Voigt configurations. Electron-hole exchange interaction is taken into account in a perturbation model on degenerate exciton states in cubic crystals to explain the splitting and the field dependence of the oscillator strengths of the J = 1 and J = 2 exciton states. Electron and hole g-values are estimated.     

Symmetry of quantum phase space in a degenerate Hamiltonian system

The structure of the global "quantum phase space" is analyzed for the harmonic oscillator perturbed by a monochromatic wave in the limit when the perturbation amplitude is small. Usually, the phenomenon of quantum resonance was studied in nondegenerate [G. M. Zaslavsky, Chaos in Dynamic Systems (Harwood Academic, Chur, 1985)] and degenerate [Demikhovskii, Kamenev, and Luna-Acosta, Phys. Rev. E 52, 3351 (1995)] classically chaotic systems only in the particular regions of the classical phase space, such as the center of the resonance or near the separatrix. The system under consideration is degenerate, and even an infinitely small perturbation generates in the classical phase space an infinite number of the resonant cells which are arranged in the pattern with the axial symmetry of the order 2&mgr; (where &mgr; is the resonance number). We show analytically that the Husimi functions of all Floquet states (the quantum phase space) have the same symmetry as the classical phase space. This correspondence is demonstrated numerically for the Husimi functions of the Floquet states corresponding to the motion near the elliptic stable points (centers of the classical resonance cells). The derived results are valid in the resonance approximation when the perturbation amplitude is small enough, and the stochastic layers in the classical phase space are exponentially thin. The developed approach can be used for studying a global symmetry of more complicated quantum systems with chaotic behavior. (c) 2000 American Institute of Physics.     

Phase transition to the resonating valence bond state

A Ginzburg-Landau expansion for the free energy functional of the resonating valence bond state is performed for the mean field approximation (MFA) and for a functional integral approach (FIA) which includes correlations. Phase diagrams obtained in both approximations are presented. The FIA differs form the MFA in three main aspects: (i) Above the mean field transition temperature an instability exists towards the formation of degenerate singlet pair states, indicating the onset of the RVB state. (ii) The extendeds-wave phase is favoured over the extendedd-wave phase. (iii) Phase fluctuations are included, destroying off-diagonal order in the absence of holes.     

在均匀强磁场中氢原子塞曼效应久期方程的简化公式

在均匀强磁场中,当氢原子的哈密顿量中B2项不能忽略时,氢原子的库仑场对称性遭到破坏,能级简并被全部解除.在应用变分法和数值法计算氢原子的能级过程中,计算十分复杂,而应用微扰法求解氢原子的能级,存在解久期方程的n2高阶行列式的困难.本文应用简并态微扰理论和球谐函数的性质,得到久期方程中非零微扰矩阵元普遍表达式.根据非零微扰矩阵元普遍表达式的性质,可以将氢原子塞曼效应久期方程的n2高阶行列式分解成1阶到n阶共n个低阶行列式的乘积,得到氢原子塞曼效应久期方程的简化公式,使得求解均匀强磁场中氢原子塞曼效应能级过程简化.而且由该公式可以得到氢原子在低能态时塞曼效应能级的解析解.根据该久期方程的简化公式计算了n=3氢原子塞曼效应一级近似能级.     

InAs量子环中类氢杂质能级

在有效质量近似下,利用微扰法研究了InAs量子环内类氢杂质基态及低激发态的能级分布。受限势采用抛物形势,在二维平面极坐标下,用薛定谔方程的精确解析解进行计算。数值计算结果显示,电子能级敏感地依赖于量子环半径,能级存在极小值,这是由于限制势采用抛物势的结果。如果减小环的半径,可以增加能级间距。第一激发态类氢杂质能级的简并没有消除,n≥2时简并的能级发生分裂并且间距随半径的增大而增大。电子能级间距还敏感地依赖于角频率并随角频率的增大而增大。第一激发态的简并没有消除,第二激发态的简并被部分地消除。在计算InAs量子环中类氢杂质的基态和低激发态的能级时,角频率改变的影响也是很深刻的。文章结果对研究量子环的光跃迁及光谱结构有重要指导意义。     

Standing spin wave modes in inhomogeneous films

A perturbation calculation for nearly degenerate states has been applied to spin wave spectra, distorted by inhomogeneity of the magnetization. The results are consistent with previous theories on the influence of parabolic or linear variations of the magnetization but they describe the experimental spectra completely and make it possible to deduce all relevant parameters.     

Valence,electronic specific heat and magnetic susceptibility of alpha-cerium

A sixfold degenerate Anderson Hamiltonian, which includes the Coulomb repulsion between localized and band states in the mean field approximation following Ramírez and Falicov, is treated in the limit of infinitely correlated 4? states and to second order in the mixing parameter. Assuming a line width Γ ≈ 0.02eV we obtain at low temperatures and 11 kbar, a valency of 3.76 and sizeable contributions from the 4? levels to the electronic specific heat and magnetic susceptibility of alpha Ce. Thus we show, that the highly correlated picture necessary to the explanation of the alpha—gamma transition by Ramírez and Falicov needs not to be abandoned in order to explain the anomalies in alpha Ce.     

Haldane-like antiferromagnetic spin chain in the large anisotropy limit

We consider the one dimensional, periodic spin chain with N sites, similar to the one studied by Haldane [1], however in the opposite limit of very large anisotropy and small nearest neighbour, anti-ferromagnetic exchange coupling between the spins, which are of large magnitude s. For a chain with an even number of sites we show that actually the ground state is non-degenerate and given by a superposition of the two Neél states, due to quantum spin tunnelling. With an odd number of sites, the Neél state must necessarily contain a soliton. The position of the soliton is arbitrary thus the ground state is N-fold degenerate. This set of states reorganizes into a band. We show that this occurs at order 2s in perturbation theory. The ground state is non-degenerate for integer spin, but degenerate for half-odd integer spin as is required by Kramers' theorem [18].     

Nuclear hyperfine interactions in non-linear semi-rigid molecules

From the expression for the hamiltonian in molecular coordinates we obtained previously, the computation of an effective hamiltonian for a nondegenerate electronic state is performed to second order in degenerate perturbation theory. We thus obtain explicitly all dominant parameters for the spin-vibration and spin-rotation interactions; in addition, the parameters associated with the interactions between the magnetic moment induced by the molecular motion and an external magnetic field are computed. The vibrational dependence of these parameters is studied and the hamiltonian is written in a form adapted to the computation of an effective hamiltonian for an arbitrary vibrational state.     

孤立的Eu2+在立方晶场中基态能级的分裂

用量子力学微扰论方法计算了Eu^2 在立方晶场中基态能级分裂的一级修正，并给出了相应能级的零级近似波矢。     

The Covariant Stark Effect

This paper examines the Stark effect, as a first order perturbation of manifestly covariant hydrogen-like bound states. These bound states are solutions to a relativistic Schrödinger equation with invariant evolution parameter, and represent mass eigenstates whose eigenvalues correspond to the well-known energy spectrum of the nonrelativistic theory. In analogy to the nonrelativistic case, the off-diagonal perturbation leads to a lifting of the degeneracy in the mass spectrum. In the covariant case, not only do the spectral lines split, but they acquire an imaginary part which is linear in the applied electric field, thus revealing induced bound state decay in first order perturbation theory. This imaginary part results from the coupling of the external field to the non-compact boost generator. In order to recover the conventional first order Stark splitting, we must include a scalar potential term. This term may be understood as a fifth gauge potential, which compensates for dependence of gauge transformations on the invariant evolution parameter.     

Classical antiferromagnet on a hyperkagome lattice

Motivated by recent experiments on Na4Ir3O8 [Y. Okamoto, M. Nohara, H. Aruga-Katori, and H. Takagi, arXiv:0705.2821 (unpublished)], we study the classical antiferromagnet on a frustrated three-dimensional lattice obtained by selectively removing one of four sites in each tetrahedron of the pyrochlore lattice. This "hyperkagome" lattice consists of corner-sharing triangles. We present the results of large-N mean field theory and Monte Carlo computations on O(N) classical spin models. It is found that the classical ground states are highly degenerate. Nonetheless a nematic order emerges at low temperatures in the Heisenberg model (N=3) via "order by disorder," representing the dominance of coplanar spin configurations. Implications for ongoing experiments are discussed.