Development of the self-consistent approximation and its application to the problem of magnetoelastic resonance in an inhomogeneous medium

Our previously proposed approximation involving both the first and second terms of the expansion of the vertex function is generalized to the system of two interacting wavefields of different physical nature. A system of self-consistent equations for the matrix Green’s function and matrix vertex function is derived. On the basis of this matrix generalization of the new self-consistent approximation, a theory of magnetoelastic resonance is developed for a ferromagnetic model, where the magnetoelastic coupling parameter ε(x) is inhomogeneous. Equations for magnetoelastic resonance are analyzed for one-dimensional inhomogeneities of the coupling parameter. The diagonal and off-diagonal elements of the matrix Green’s function of the system of coupled spin and elastic waves are calculated with the change in the ratio between the average value ε and rms fluctuation Δε of the coupling parameter between waves from the homogeneous case (ε ≠ 0, Δε = 0) to the extremely randomized case (ε = 0, Δε ≠ 0) at various correlation wavenumbers of inhomogeneities k _c. For the limiting case of infinite correlation radius (k _c = 0), in addition to approximate expressions, exact analytical expressions corresponding to the summation of all diagrams of elements of the matrix Green’s function are obtained. The results calculated for an arbitrary k _c value in the new self-consistent approximation are compared to the results obtained in the standard self-consistent approximation, where only the first term of the expansion of the vertex function is taken into account. It is shown that the new approximation corrects disadvantages of the Green’s functions calculated in the standard approximation such as the dome shape of resonances and bends on the sides of resonance peaks. The appearance of a fine structure of the spectrum in the form of a narrow resonance on the Green’s function of spin waves and a narrow antiresonance on the Green’s function of elastic waves, which was previously predicted in the standard self-consistent approximation, is confirmed. With an increase in the parameter k _c, the Green’s functions calculated in the standard and new approximations approach each other and almost coincide with each other at k _c/k ≥ 0.5. At the same time, the results of this work indicate that the new self-consistent approximation has a certain advantage for studying the problems of stochastic radiophysics in media with long-wavelength inhomogeneities (small k _c values), because it describes both the shape and width of peaks much better than the standard approximation.     

Crossing resonance of stochastically interacting wave fields

The dynamic susceptibilities (Green’s functions) of the system of two interacting wave fields of different physical natures with a stochastically inhomogeneous coupling parameter between them with zero mean value have been examined. The well-known self-consistent approximation taking into account all diagrams with noncrossing correlation/interaction lines has been generalized to the case of stochastically interacting wave fields. The analysis has been performed for spin and elastic waves. The results obtained taking into account the processes of multiple scattering of waves from inhomogeneities are significantly different from those obtained for this situation earlier in the Bourret approximation [R.C. Bourret, Nuovo Cimento 26, 1 (1962)]. Instead of frequencies degeneracy removal in the wave spectrum and the splitting of resonance peaks of dynamic susceptibilities, a wide single-mode resonance peak should be observed at the crossing point of the unperturbed dispersion curves. The fine structure appears at vertices of these wide peaks in the form of a narrow resonance on the Green’s-function curve of one field and a narrow antiresonance on the vertex of the Green’s-function curve of the other field.     

Bulk plasma waves in a randomly inhomogeneous conductor

The modification of the spectrum and damping of bulk plasma waves due to three-dimensional random inhomogeneities of the density of a degenerate electron gas in a conductor have been investigated using the averaged Green??s function method. The dependences of the frequency and damping of the averaged plasma waves, as well as the position ?? _m and width ???? of the peak of the imaginary part of the Fourier trans-form of the averaged Green??s function, on the wave vector k have been determined in the self-consistent approximation, which makes it possible to take into account multiple scattering of plasma waves by inhomogeneities. It has been found that, in the long-wavelength region of the spectrum, the decrease revealed in the frequency of the plasma waves is caused by the inhomogeneities, which agrees qualitatively with the behavior of the position of the peak ?? _m . In the range of large values of the correlation length of inhomogeneities and small values of k, the damping of the plasma waves tends to zero, whereas the width of the peak ???? remains finite, which is due to the nonuniform broadening. A comparison with the data of numerical calculations has been performed.     

Sums of products of Coulomb wave function over degenerate states

The sums of products of Coulomb wave function over degenerate states are expressed in terms of quadratic forms that depend on the wave function of only one state with zero orbital angular momentum l = m = 0. These sums are encountered in many fields in the physics of atoms and molecules, for example, in investigations of the perturbation of degenerate atomic energy levels of a small potential well, a delta-function potential. The sums were found in an investigation of the limit of the Coulomb Green’s function G(r, r′, E), where the energy parameter E approaches an atomic energy level: E → E _n , E _n = ?Z ²/2n ². The Green’s function found by L. Hostler and R. Pratt in 1963 was used. The result obtained is a consequence of the degeneracy of the Coulomb energy levels, which in turn is due to the four-dimensional symmetry of the Coulomb problem.     

Electromagnetic waves in a randomly inhomogeneous Josephson junction

Spectrum modification and damping of Josephson plasma waves induced by random inhomogeneities of the critical current through the superconductor contact and the averaged Green function of such excitations are analyzed. In the self-consistent approximation that makes it possible to take into account multiple wave scattering on the inhomogeneities, the frequency and damping of averaged waves, as well as position ν _m and peak width Δν of the Fourier transform imaginary part of the averaged Green function, are determined as functions of wavevector k. The evolution of such functions with the variation of the correlation radius and the relative r.m.s. fluctuations of inhomogeneities is studied. The inhomogeneity-induced wave frequency decrease observed in the long wavelength spectral region qualitatively agrees with the ν _m behavior. It is established that in the case of “long-range” inhomogeneities, the linear dependence of damping on k changes to the inversely proportional one, and damping tends to zero as k → 0, while Δν at small k attains its maximal values due to nonuniform broadening. In the presence of “short-range” inhomogeneities, the wave damping and Δν are found to be similar functions of k. The results are compared to the numerical calculation data.     

High-frequency susceptibility of a superlattice with 2D inhomogeneities

We investigate the high-frequency susceptibility (Green function) of an initially sinusoidal 1D superlattice with 2D phase inhomogeneities that model the deformations of the interfaces between the superlattice layers. For waves propagating along the superlattice axis (the geometry of a photon or magnon crystal), we have found a peculiar behavior of the imaginary part of the Green function that consists in a significant difference between the peaks corresponding to the edges of the band gap in the wave spectrum. The peak corresponding to the lower-frequency band edge remains essentially unchanged as the root-mean-square fluctuation of the 2D inhomogeneities γ₂ increases, while the peak corresponding to the higher-frequency band edge broaden and decreases sharply in height until its complete disappearance with increasing γ₂. This behavior of the peaks corresponds to a band gap closure mechanism that differs from the traditional one characteristic of 1D and 3D inhomogeneities. These effects can be explained by a peculiarity of the energy conservation laws for the incident and scattered waves for 2D inhomogeneities in a 1D superlattice.     

Electromagnetic waves with a negative group velocity in a randomly inhomogeneous Josephson junction

Electromagnetic waves in a randomly inhomogeneous Josephson junction have been investigated by the averaged Green’s function method for a nonmonotonic decay of the correlations of inhomogeneities. Modifications of the spectrum and the decay of these excitations caused by spatial fluctuations of the critical current of the Josephson junction have been studied. The regions of the values of the frequency, the wave number, and the stochastic parameters of the medium, at which the waves have a negative group velocity, have been determined.     

The QCD sum rule approach for the semileptonic decay of the D or B meson into a light meson and leptons

We use the method of QCD sum rules to treat the semileptonic weak decay of the D or B meson into a light meson and leptons. To obtain the transition form factors, we adopt the two-point Green’s function in the presence of an external vector or axial-vector field. We find that this method can be related approximately to the traditional three-point Green’s function in the heavy quark limit (m _Q → ∞). Unlike some existing QCD sum rule calculations, our results indicate that the form factors have simple dipole or monopole behavior. We obtain results on the various form factors of the semileptonic decay of D and B mesons into a light meson and investigate various decay processes such as B?⁰ → π ⁺ τ _^?ν?_τ and B?⁰ → ρ ⁺ τ^～ν?_τ. The method allows us to take into account nonperturbative strong interaction effects, thereby providing a more reliable determination of the Cabibbo-Kobayashi-Maskawa matrix elements from the experimental data.     

The nonlinear dispersion of Rayleigh waves

Rayleigh waves in linear elasticity are non-dispersive-all profiles propagate without change of form, at the speed c_R Previously, the author has determined periodic non-distorting waveforms for nonlinear elastic surface waves. They are far from sinusoidal. For each waveform, the difference between the phase speed c and cR is proportional to the wave steepness (the ratio amplitude/wavelength). The present paper shows, using Whitham's methods for analysing modulations of wavetrains, that gradual changes of amplitude and wavelength of these nonlinear Rayleigh waves propagate in a particularly simple manner. The loci of constant phase speed always propagate as a simple wave, with group velocityc_G = G(c). The phase curves also are characteristic curves of the modulation equations.It is shown that these two properties are general properties of the modulation of waveforms having phase speed depending only on wave steepness. Such waveforms arise from physical systems with no intrinsic scales of length or time.     

Structure of the Gauge Invariant Quark Green’s Function in QCD2

We study, in two-dimensional QCD and in the large-N _c limit, the properties of the gauge invariant quark Green’s function, defined with a path-ordered phase factor along a straight line. The analysis is done by means of an exact integrodifferential equation. The Green’s function is found to be infrared finite, with singularities represented by an infinite number of threshold type branch points with a power ?3/2, starting at positive mass squared values. Its expression is analytically determined.     

Effect of the correlation properties of one-and three-dimensional inhomogeneities on the high-frequency magnetic susceptibility of sinusoidal superlattices

The effect of one-(1D) and three-dimensional (3D) inhomogeneities on the high-frequency magnetic susceptibility at the boundary of the first Brillouin zone of a ferromagnetic superlattice is studied. The study is performed with an earlier developed method of random spatial modulation (RSM) of the superlattice period. In this method, structural inhomogeneities are described in terms of the random-phase model, in which the phase depends on three coordinates in the general case. The frequency spacing Δν_m between two peaks in the imaginary part of the averaged Green’s function, which characterizes the gap width in the frequency spectrum at the boundary of the Brillouin zone, is calculated as a function of both the root-mean-square fluctuations γ_i and the correlation wavenumbers η_i of phase inhomogeneities (i = 1 and 3 for 1D and 3D inhomogeneities, respectively). The function Δν_m(γ₁, η₁) for 1D inhomogeneities is shown to be symmetric with respect to interchanging the variables γ ₁ ² and η₁, whereas the function Δν_m(γ₃, η₃) for 3D inhomogeneities is strongly asymmetric with respect to interchanging γ ₂ ³ and η₃. This effect is associated with the difference in form between the correlation functions of 1D and 3D inhomogeneities and can be used to determine the dimensionality of inhomogeneities from the results of spectral studies of such superlattices.     

Spin density wave magnetism in copper—manganese alloys

The incommensurate magnetization waves (IMW) occuring at the wave vector $\text{Q = (1, 0.5 ? δ, 0)}\text{2π}\text{a}$ and equivalent positions in reciprocal space in Cu_1?xMn_x have been studied as a function of temperature, wavevector, frequency and composition, using high-resolution, unpolarized neutron scattering techniques. We find that the elastic component of the scattering cross section at these incommensurate wavevectors approaches zero in the vicinity of the “spin glass” freezing temperature, T_f, closely resembling that expected for an order parameter on approach to the critical point. We suggest that the interaction between Mn atoms is long-range and intimately connected to a spin density wave instability.     

反射情况下X射线衍射方程的Green函数解法

对半无穷厚晶体用推迟Green函数G^(r),解出X射线在反射情形下的场值D_h,对有限厚晶体,用G^(r)和超前Green函数G^(a)能类似地求解,将这些结果与其它作者用Rie-mann函数或Fourier积分得到的结果作了比较,吻合是令人满意的。 关键词：     

Electronic and high pressure elastic properties of RECd and REHg (RE=Sc,La and Yb) intermetallic compounds

Structural, electronic, elastic and mechanical properties of Cd and Hg based rare earth intermetallics (RECd and REHg; RE=Sc, La and Yb) have been investigated using the full-potential linearized augmented plane-wave (FP-LAPW) method within the density-functional theory (DFT). The ground state properties such as lattice constant (a₀), bulk modulus (B) and its pressure derivative (B′) have been obtained using optimization method and are found in good agreement with the available experimental results. The calculated enthalpy of formation shows that LaHg has the strongest alloying ability and structural stability. The electronic band structures and density of states reveal the metallic character of these compounds. The structural stability mechanism is also explained through the electronic structures of these compounds. The chemical bonding between rare earth atoms and Cd, Hg is interpreted by the charge density plots along (1 1 0) direction. The elastic constants are predicted from which all the related mechanical properties like Poisson’s ratio (σ), Young’s modulus (E), shear modulus (G_H) and anisotropy factor (A) are calculated. The ductility/brittleness of these intermetallics is predicted. Chen’s method has been used to predict the Vicker’s hardness of RECd and REHg compounds. The pressure variation of the elastic constants is also reported in their B₂ phase.     

Recursive Green functions technique applied to the propagation of elastic waves in layered media

Guided by similarities between electronic and classical waves, a numerical code based on a formalism proven to be very effective in condensed matter physics has been developed, aiming to describe the propagation of elastic waves in stratified media (e.g. seismic signals). This so-called recursive Green function technique is frequently used to describe electronic conductance in mesoscopic systems. It follows a space-discretization of the elastic wave equation in frequency domain, leading to a direct correspondence with electronic waves travelling across atomic lattice sites. An inverse Fourier transform simulates the measured acoustic response in time domain. The method is numerically stable and computationally efficient. Moreover, the main advantage of this technique is the possibility of accounting for lateral inhomogeneities in the acoustic potentials, thereby allowing the treatment of interface roughness between layers.     

Extraction of the asymptotic normalization coefficient for the first 2+ level of 16O from the analysis of α12C scattering on the basis of analytical approach

The information about the nuclear vertex constant G ₁₂ for the ¹⁶O(6.917 MeV, 2⁺) ? α + ¹²C vertex and the related asymptotic normalization coefficient C ¹² of the wave function of the first excited state of the ¹⁶O nucleus with the angular momentum J = 2 and positive parity is extracted on the basis of the phase analysis data for the α¹²C scattering using the N/D equations, with allowance for the Coulomb interaction effects.     

InBO3 and ScBO3 at high pressures: An ab initio study of elastic and thermodynamic properties

We have theoretically investigated the elastic properties of calcite-type orthoborates ABO₃ (A=Sc and In) at high pressure by means of ab initio total-energy calculations. From the elastic stiffness coefficients, we have obtained the elastic moduli (B, G and E), Poisson's ratio (ν), B/G ratio, universal elastic anisotropy index (A_U), Vickers hardness, and sound wave velocities for both orthoborates. Our simulations show that both borates are more resistive to volume compression than to shear deformation (B>G). Both compounds are ductile and become more ductile, with an increasing elastic anisotropy, as pressure increases. We have also calculated some thermodynamic properties, like Debye temperature and minimum thermal conductivity. Finally, we have evaluated the theoretical mechanical stability of both borates at high hydrostatic pressures. It has been found that the calcite-type structure of InBO₃ and ScBO₃ becomes mechanically unstable at pressures beyond 56.2 and 57.7 GPa, respectively.     

Calculation of the electroelastic Green’s function of the hexagonal infinite medium

The electroelastic 4 × 4 Green’s function of a piezoelectric hexagonal (transversely isotropic) infinitely extended medium is calculated explicitly in closed compact form ((73) ff. and (88) ff., respectively) by using residue calculation. The results can also be derived from Fredholm’s method [2]. In the case of vanishing piezoelectric coupling the derived Green’s function coincides with two well known results: Kröner’s expressions for the elastic Green’s function tensor [4] is reproduced and the electric part then coincides with the electric potential (solution of Poisson equation) which is caused by a unit point charge. The obtained electroelastic Green’s function is useful for the calculation of the electroelastic Eshelby tensor [16].     

Irreducible kernels and nonperturbative expansions in a theory with purem →m interaction

Recent results on the structure of theS matrix at them-particle threshold (m≧2) in a simplifiedm→m scattering theory with no subchannel interaction are extended to the Green functionF on the basis of off-shell unitarity, through an adequate mathematical extension of some results of Fredholm theory: local two-sheeted or infinite-sheeted structure ofF arounds=(mμ)² depending on the parity of (m?1)(ν?1) (where μ>0 is the mass and ν is the dimension of space-time), off-shell definition of the irreducible kernelU which is the analogue of theK matrix in the two different parity cases (m?1)(ν?1) odd or even, and related local expansion ofF, for (m?1)(ν?1) even, in powers of σ_β ln σ(σ=(mμ)²?s). It is shown that each term in this expansion is the dominant contribution to a Feynman-type integral in which each vertex is a kernelU. The links between the kernelU and Bethe-Salpeter type kernelsG of the theory are exhibited in both parity cases, as also the links between the above expansion ofF and local expansions, in the Bethe-Salpeter type framework, ofF _λ in terms of Feynman-type integrals in which each vertex is a kernelG and which include both dominant and subdominant contributions.     

Calculation of the off-diagonal elements of a two-photon laser

An expression for the off-diagonal matrix elements of a two-photon laser is presented, starting directly from the equation of motion for ρ_nm. The cavity loss mechanism has been simulated by a single-photon process. In the case of a two-photon laser well above threshold, an expression for the lowest eigenvalue of the ρ_nm has been found. Saturated two-photon emission has been also treated.