Degenerate perturbation theory and its application to the Hubbard model

Projection operators are incorporated in the canonical transformation to derive an analytical infinite series of a degenerate perturbation expansion. The theory is used to calculate the ground state energy of a half-filled s-band Hubbard model to seventh order.     

互补变分原理及其在微扰理论近似中的应用

以正则变分和线性变分函数为基础，对互补变分原理作了论证，推导出二阶能量修正的上界和不受任何条件限制的下界，对具体计算方法作了详细的研究，得出互补变分原理在微扰理论近似中的应用，所求氢原子和极化率结果比一般的发法的微扰法所得结果更接近于实验值，并指出这理论可以推广应用到激发态或处理高阶修正问题。     

The method of exchange perturbation theory as applied to magnetic ordering in high-T c materials

We unify the method of exchange perturbation theory for multicenter systems. For the case of exchange degeneracy in the total spin of the system we give a secular equation that is more compact and convenient for calculations than those obtained earlier. On the basis of this formalism we develop an algorithm for calculating the Heisenberg parameter for magnetic materials. Finally, we calculate the characteristics of antiferromagnetic transitions for the high-T _c materials La_2−x MeCuO₄ and YBa₂Cu₃O₆. Zh. éksp. Teor. Fiz. 113, 2129–2147 (June 1998)     

Quantum mechanical calculation of multi-time-correlation functions and its application to the laser theory

Quantum mechanical multi-time-correlation functions are derived and applied to laser theory. The correlation functions for the laser field amplitudes and intensities are calculated. Far above the threshold region the latter correlation function shows damped oscillations.     

New approach to perturbation theory of many-particle systems

We derive an infinite hierarchy of integral equations for the Green functions of a many-particle system. This set of equations forms the basis of a unified approach to the perturbation theory of many boson and many fermion systems and avoids the introduction of the adiabatic hypothesis. It is demonstrated how a well-known ground state perturbation theory of a system of interacting fermions is obtained without introducing disconnected diagrams. It is shown that the formalism allows a self-consistent determination of the condensate Green function of a condensed Bose system and a derivation of the Beliaev, Hugenholtz, and Pines result for the single-particle k 0 Green function is given. A new self-consistent equation for the k = 0 Green function is solved to yield the well-known self-energy relation ₁₁ – ₀₂ = which plays the role of a self-consistency condition on the theory.     

Low temperature nuclear orientation and its application to magnetic systems

This article contains an outline of the basic principles of low temperature nuclear orientation LTNO and of nuclear magnetic resonance on oriented nuclei NMR/ON. A summary is given of the experimental requirements and constraints of these methods followed by a survey of their applications to the study of magnetism in solids. More detailed consideration is given to relaxation topics, including fast passage and pulsed RF techniques, and to the variety of methods now available, based on nuclear orientation and resonance, for the separate extraction of magnetic dipole and electric quadrupole interaction strengths when they occur together.     

High-order perturbation theory for the hydrogen atom in a magnetic field

The states of a hydrogen atom with principal quantum numbers n⩽3 in a constant uniform magnetic field ℋ are studied. Coefficients in the expansion of the energy of these states in powers of ℋ² up to the 75th order are obtained. Series for the energies of the states and the wave functions are summed to values of ℋ on the order of the atomic magnetic field. A generalization of the moment method upon which these calculations are based can be used in other cases in which a hydrogen atom is perturbed by a potential with a polynomial dependence on the coordinates. Zh. éksp. Teor. Fiz. 113, 550–562 (February 1998)     

A new method for calculation of the magnetic properties in one- and two-dimensional spin systems with anisotropic Heisenberg exchange

A new approximation method is proposed for the calculation of the magnetic susceptibility of one-dimensional assembly of spins and the critical temperature of two-dimensional one both with the anisotropic Heisenberg exchange. In a linear chain system, every spins are grouped into pairs of adjacent spins (pair-approximation) or clusters of adjacent three spins ((q+1)-approximation), and the partition function of the total spin system is approximated as a sum of products of the partitions functions for the pairs or the clusters. Then the partition function of the anisotropic Heisenberg spin system is shown to reduce into a form of the Ising spin system with modified coupling constants. The exact result for the Ising chain system enables us to obtain an analytical expression for the magnetic susceptibility of anisotropic Heisenberg chain system. The same approximations are also applied to two-dimensional lattices, and the critical temperatures of the square, triangular, and honeycomb lattices with anisotropic Heisenberg exchange are calculated as a function of anisotropy parameter. The results are compared with those of the existing theories and shown to be quite excellent.     

Self-consistent perturbation theory for the vibrational spectra of certain disordered systems

The effect of coupling parameter fluctuations (quantitative disorder) on the vibrational spectrum of a solid is investigated. Since small deviations from crystalline order already turn out to lead to considerable broadening of the crystalline spectrum, a self-consistent perturbation scheme is developed similar to the coherent potential approximation for electronic systems. An approximate equation is obtained in which disorder is described in terms of a single dimensionless parameter which is a measure of the mean square fractional deviations of the coupling parameters from their average values. The equation is solved self-consistently by iteration. The final result is a convolution expression for the amorphous spectrum in which all van Hove singularities are smeared out except the ones at zero frequency and at the upper cutoff of the spectrum. Numerical results are obtained for silicon using a Keating crystalline density of states and assuming that the average values of the coupling parameters are identical to the crystalline ones. The maxima of the crystalline spectrum are broadened but qualitatively retained to a larger extent than in a simple convolution of the spectrum with a Gaussian.     

Multiparticle perturbation theory and an accurate calculation of parity nonconservation in cesium

A method of calculating higher-order correlation corrections, using Green's functions and the Feynman diagrammatic technique, is developed. A basis of the single-electron orbitals is computed using the relativistic Hartree-Fock method. The interaction of an atom with an external field is computed by solving the time-dependent Hartree-Fock equations. In the methodology presented, we consider all the second-order correlation corrections and the dominating classes of higher order diagrams: the screening of the Coulomb interaction of electrons, particle-hole interaction and mass operator iterations. The calculation of the energy levels, the intervals of hyperfine structure and the amplitudes of the allowed EI-transitions in C_s shows that the method developed ensures precision at the 0.1–1% level. A calculation of the parity nonconservation of the El-amplitude of the transition 6s–7s in Cs is produced. The result <6s¦D_z¦7s> = –(0.91 ± 0.01)·10^–11 i¦e¦a^B (–Q_W/N) is obtained.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 108–119, August, 1990.     

Finite perturbation theory-density functional theory calculation of the spin-dipolar contribution to NMR spin-spin coupling constants

In this work an implementation of the FPT-DFT approach for calculating the spin-dipolar contribution to NMR spin-spin coupling constants is presented. This method was tested in a set of small molecules, giving results in excellent agreement when comparing them with values taken from the literature, which were obtained with state-of-the-art calculations. To obtain an insight into the relative importance of the spin-dipolar contribution in unsaturated compounds, calculations of J(F,C), J(F,F) and J(F,H) couplings in 1,2-, 1,3-, and 1,4-difluorobenzenes were performed. An important spin-dipolar contribution to ³ J(F, F) and ⁵ J(F,F) was found, suggesting that this term might be important in some cases. When performing DFT calculations the non-singlet instabilities usually found in unsaturated compounds are overcome.     

Phase separation in La-Pr manganites and its evolution in a magnetic field

The self-consistent harmonic oscillator model including the three-dimensional cranking term is extended to describe collective excitations in the random phase approximation. It is found that quadrupole collective excitations associated with wobbling motion in rotating nuclei lead to the appearance of two-or three-dimensional rotation.     

A new perturbation method to the Tent map and its application

Disturbance imposed on the chaotic systems is an effective way to maintain its chaotic good encryption features. This paper proposes a new perturbation method to the Tent map. First it divides the Tent map domain into 2^N parts evenly and selects a particular part from them, then proliferates the Tent map mapping trajectory of this particular part, which can disturb the entire system disturbance. The mathematical analysis and simulated experimental results prove that the disturbed Tent map has uniform invariant distribution and can produce good cryptographic properties of pseudo-random sequence. These facts avoid the phenomenon of short-period caused by the computer's finite precision and reducing the sequence's dependence on the disturbance signal, such that effectively compensate for the digital chaotic system dynamics degradation.     

永磁体空间磁场的分析计算及其在永磁磁力轴承中的应用

在介绍三种永磁体空间磁场计算模型的基础上,利用泛函理论分别推导出等效磁荷模型和等效电流模型对应的变分形式,并就等效磁荷模型详细地介绍了有限元法．由于等效磁荷模型使用仅有一个自由度的标量磁位,因而计算起来比具有三个自由度的矢量磁位的等效电流法更简便．从永磁磁力轴承磁场的计算算例中可以看出,用等效磁荷模型的有限元法计算永磁体空间磁场是非常简便和有效的．     

布朗运动理论及其在复杂气候系统研究中的应用

文章将从非平衡态统计物理发展和应用的角度,介绍德国科学家哈塞尔曼荣获2021年诺贝尔物理学奖的研究工作——基于布朗运动理论,建立了描述气象(天气)影响气候长期演化的随机气候学模型,并建立了寻求影响气候主因的最优指纹方法,从而能够分辨出人类活动和自然界局部改变对气候这一复杂系统的影响。哈塞尔曼的工作本质上是理论物理在实际复杂系统领域的成功应用,他采用的基础物理方法——布朗运动理论是我国杰出女物理学家王明贞和其导师乌伦贝克在20世纪40年代基于爱因斯坦的工作发展起来的^[1,2]。文章将介绍布朗运动理论的发展及其相关的非平衡统计物理思想的当代发展,以展示哈塞尔曼如何把相关的物理理论巧妙地用于气候长期预测的实际应用研究：(1)建立了快变的局部“气象”变量涨落通过耗散涨落关系影响缓变的整体气候变量的基础理论;(2)通过最优指纹方法,寻找局部“噪音”和外驱动力影响气候演化的关键要素。