Elastic interaction potential in solid solutions with cubic symmetry

On the basis of a microscopic approximation, within which three parameters of interatomic binding (according to the number of elastic constants of a cubic crystal) are taken into account, an approximation for the coefficients of the expansion has been obtained for the elastic interaction potential in vs elastic constants of a cubic crystal. An analysis of the kind of dependencies of the expansion coefficients on the direction has been carried out. It has been shown that can have an accidental saddle anomaly in planes of the type 110, in addition to extrema in high-symmetry directions of the type <100>, <110>, <111>. Coefficient B always takes negative values for bcc crystals near <100> directions. An approximation has been found for the elastic interaction potential vs elastic moduli of a cubic crystal, starting from a microscopic approach.Translated from Izvestiya Vysshikh Uchebnykh Zavenenii, Fizika, No. 2, pp. 20–24, February, 1982.     

一类三次方对称离散混沌系统的分岔控制

通过分析对称性破缺分岔机制, 采用了一个直接的、有效的线性控制器, 精确控制了一类三次方对称离散混沌系统发生对称性破缺分岔和倍周期分岔时分岔点的位置. 进而分析了系统对初始值的敏感性和对称性, 选择合适的吸引域, 将对称性破缺分岔进行进一步控制, 从而使得对称性破缺分岔所缺解枝得以恢复. 数值结果表明了该控制器的有效性. 关键词： 离散混沌系统 对称性破缺 倍周期 分岔控制     

Scissors Modes in crystals with cubic symmetry

We recently suggested that the Scissors Mode (a collective excitation in which one system rotates with respect another one conserving its shape) can occur in crystals with axially symmetric atoms as a precession of these atoms around the anisotropy axis of their cells, giving rise to a form of dichroism. In the present paper we investigate how the Scissors Mode can be realized in crystals with cubic symmetry and evaluate its photo-absorption cross-section. This turns out to be of the same order of magnitude as that for crystals with axially symmetric atoms, but does not exhibit any correlation between the direction of the photon and the axes of the cell.     

Ferromagnetism of binary compounds with cubic symmetry

Based on the idea of a strong interaction within the same unit cell, the possible existence of a ferromagnetic instability in a system with jumps from transition element cations to non-transition element anions and vice versa is established. A phase diagram is constructed for the ferromagnetic ordering as a function of the degree of filling, n _p and n _d , of the p ⁶-and d ¹⁰-shells of non-transition and transition elements, respectively. Zh. éksp. Teor. Fiz. 115, 1393–1410 (April 1999)     

平面对称黑洞的统计熵

避开求解各种粒子波动方程的困难,直接应用量子统计的方法,计算平面对称黑面背景下玻色场与费米场的配分函数,得到黑面熵的积分表达式.然后应用改进的brickwall方法膜模型,计算黑面视界所对应的统计熵.在所得结果中当所取的积分下限和上限都趋于视界上时,可得到黑面熵与相应黑面视界面积成正比的关系,不存在原brickwall方法中的舍去项与对数发散项.整个计算过程,物理图像清楚,计算简单,为研究黑洞熵提供了一条简捷的新途径 关键词： 量子统计 膜模型 黑面熵     

Quantum fluctuations in a two-dimensional antiferromagnet with four-spin interaction of cubic symmetry

The excitation spectrum of a non-Heisenberg 2D antiferromagnet with the four-spin interaction of cubic symmetry has been calculated in the first order of 1/2S. It has been shown that, for weak anisotropy, the Néel state is destroyed by quantum fluctuations. The phase diagrams showing the stability regions of the Néel phase in the space of spin-anisotropy parameters have been plotted.     

Calculation of the spin-lattice coupling coefficients in cubic symmetry

The relationships between spin-lattice coupling coefficients G₁₁, G₄₄ in cubic symmetry and the zero-field splittings in low symmetry have been put forward and hence the simple methods of calculating these coefficients from the formulae of zero-field splittings are given. According to these, the coefficient G₄₄ can be obtained very easily from two cases, one from the derivative of zero-field splitting D in trigonal symmetry with respect to the bonding angle β and another from the derivative of splitting E in rhombic symmetry with respect to the angle θ. So, one can, in a certain degree, check whether the formulae of D in trigonal field and E in rhombic field based on different mechanisms and models are consistent and reliable by comparing the formulae of G₄₄ obtained from the two cases.     

Tunnelling states in a potential of hexagonal symmetry

The tunnel splitting of the ground state multiplet in a potential of the form V₀cos 6φ is calculated both in the weak perturbation and in the high barrier limit. In the latter limit a true variational calculation is performed and this gives better results than obtained by previous methods.     

Relaxation time of a Brownian rotator in a potential with nonparabolic barriers

The extension of the Kramers theory of the escape rate of a Brownian particle from a potential well to the entire range of damping proposed by Mel’nikov and Meshkov [V.I. Mel’nikov, S.V. Meshkov, J. Chem. Phys. 85 (1986) 1018] is applied to the inertial rotational Brownian motion of a fixed axis rotator in a potential V(θ)=−K₁cos2θ−K₂cos4θ, where θ is the angle specifying the orientation of the rotator and K₁ and K₂ are constants. It is shown that in the neighbourhood of K₁∼4K₂ (flat barrier), the Mel’nikov-Meshkov method must suitably be adapted so that the effect of a nonparabolic barrier top can be correctly accounted for in the calculation of the relaxation time. The results obtained are compared with numerical calculations of the longest relaxation time (inverse smallest nonvanishing eigenvalue) using a matrix continued fraction algorithm and reasonable agreement is obtained for K₁≥4K₂ and all values of the dissipation parameter.     

Statistical dynamics

A way is suggested of incorporating the exact dynamics of a system into a statistical framework which is self-contained for low-order distribution functions.     

Anisotropy of the electron g factor in semiconductors with cubic symmetry

The spin-orbit corrections to electronic states in bulk cubic semiconductors without the center of inversion in an ultraquantum magnetic field are investigated. It is shown that the spin-orbit interaction results in a shift of the Landau levels and the appearance of additional terms in the relationship for the electron g factor. The corrections to the g factor lead to a deviation of the macroscopic magnetization from the direction of the magnetic field, the dependence of the spin resonance frequency on the magnetic field orientation with respect to the principal crystallographic axes, and anisotropy of the spin relaxation through the D’yakonov-Perel’ mechanism.     

On the theory of ferromagnetism in transition metals with cubic symmetry

The idea of strong interaction within the same unit cell is used to establish the possibility of the existence of ferromagnetic instability in a system with jumps between cations of transition elements. The phase diagram of the existence of the ferromagnetic ordering as a function of the average number of holes (h _d ) in the 3d¹⁰ shell of transition elements is constructed.     

Statistical theory of slip channels in body-centered cubic metals

Received: 26 July 1996/Accepted: 7 October 1996     

Symbolic dynamics of the cubic map

A symmetric cubic map on the interval describing isolated stable or bistable orbits and different kind of bifurcation was analyzed. Stable orbits were presented by itineraries, permutation parentheses and matrices. Itineraries were used to order the cycles with respect to the parameter and also to order the coordinates of the cycle in the interval. Linear symbolic dynamics was introduced to study the periodic unstable points coexisting with stable orbits by means of a matrix of intervals. The non-zero entries of these matrices have an N-shape corresponding to the N-shape of the cubic. The characteristic polynomial of the matrix of intervals was in one-to-one correspondence with the itinerary. Equations to calculate the number of different kind of orbits were explicitly written and used to calculate those numbers for a small number of periods.