Vector boson in the constant electromagnetic field

The propagator and the complete sets of in-and out-solutions of the wave equation, together with the Bogoliubov coefficients relating these solutions are obtained for the vector W-boson (with the gyromagnetic ratio g=2) in a constant electromagnetic field. When only the electric field is present, the Bogoliubov coefficients are independent of the boson polarization and are the same as for the scalar boson. For the collinear electric and magnetic fields, the Bogoliubov coefficients for states with the boson spin perpendicular to the field are again the same as in the scalar case. For the W ^? spin parallel (antiparallel) to the magnetic field, the Bogoliubov coefficients and the one-loop contributions to the imaginary part of the Lagrange function are obtained from the corresponding expressions for the scalar case by the substitution m ² → m ²+2eH (m ² → m ²-2eH). For the gyromagnetic ratio g=2, the vector boson interaction with the constant electromagnetic field is described by the functions that can be expected by comparing the scalar and Dirac particle wave functions in the constant electromagnetic field.     

Second-order terms in the phonon-phason dynamic matrix of an icosahedral quasicrystal

They fourth-order terms (in the wave vector components) of the phonon-phason dynamic matrix are obtained for an icosahedral quasicrystal. In this order, the dynamic matrix has nine independent coefficients: three phonon-phonon, three phason-phonon, and three phason-phason coefficients. The number of independent coefficients in the phonon block of the constructed dynamic matrix is greater by unity than that for an isotropic medium. The corresponding features of acoustic phonon dispersion in the i-AlPdMn alloy are considered. It is shown that when the fourth-order terms are taken into account, the intensity of diffuse scattering in the vicinity of Bragg reflections decreases in accordance with the law α/(q ²+βq ⁴), where q is the distance to a reflection in the reciprocal space and coefficients α and β depend on the direction of vector q.     

Multiphonon contribution to the structure factor of metals

The structure factor of Na is calculated including two-phonon terms and the Debye-Waller factor. The result is compared with the one-phonon approximation usually employed to evaluate the electronic transport coefficients. This multiphonon contribution can amount to 13 per cent at the melting point and 10 per cent at room temperature in the transport sensitive region of wave vector 1.5 k_F < q < 2 k_F, where k_F is the Fermi wave vector. We conclude that calculations of electronic transport coefficients of metals intended to attain a precision better than 10 per cent above the Debye temperature must take into account the contributions of the Debye-Waller factor and the two phonon terms.     

The quantum mechanical toda lattice

The aim of this paper is to establish the exact quantization conditions for the three-body Toda lattice. The Hamiltonian consists of the kinetic energy for three particles in one dimension, and of the potential energy which couples each particle to its two companions through an exponential spring. After eliminating the center of mass motion, one is left with a system of two degrees of freedom and two constants of motion, the total energy E and a third integral A which commute. Nevertheless, no transformation has been found to separate the classical equations of motion or Schrödinger's equation. The wave function is written as a double Laurent series. Its coefficients have to satisfy two sets of recursion relations on a triangular grid where each set insures that we have a simultaneous eigenfunction of E and A. The condition for the convergence of this series can be expressed as the vanishing of a tridiagonal infinite determinant with 1 in the diagonal and the inverse of a third-order polynomial in the first off-diagonals. The coefficients in this polynomial are E and A, and the variable corresponds to a component of the wave vector associated with the wave function. This determinant can be treated exactly as Hill's, and yields the 3 components. The condition for the square integrability of the wave function requires the phase angle of the principal minors to be equal to 0, $\text{π}\text{3}$, or $\text{2π}\text{3}$ according as the representation of the cyclic groups, for each component of the wave vector. But the third condition follows from the two others. The analogy with the corresponding two-body problem is pointed out.     

Magnetooptical properties of a ferromagnetic superlattice

Transmission and reflection of a normally incident wave from a magnetic superlattice consisting of 2N ferromagnetic layers with alternating orientation of the magnetization vector are considered. The characteristic matrix of a superlattice relating wave amplitudes at the entrance to the system and at the exit from it is calculated in the closed form and Jones matrices determining all the basic magnetooptical characteristics of the structure (transmission and reflection coefficients, the degree of polarization of transmitted and reflected waves, and so on) are constructed. A significant dependence of these characteristics on the number of layers is demonstrated.     

Optical anisotropy of InAs/GaSb broken-gap quantum wells

We investigate in detail the optical anisotropy of absorption of linearly polarized light in InAs/GaSb quantum wells grown on GaSb along the [001] direction, which can be used as an active region of different laser structures. The energy level positions, the wave functions, the optical matrix elements, and the absorption coefficients are calculated using the eight-band k · p model and the Burt-Foreman envelope function theory. In these calculations, the Schr?dinger and Poisson equations are solved self-consistently taking the lattice-mismatched strain into account. We find that a realistic Hamiltonian, which has the C _2v symmetry, results in considerable anisotropy of optical matrix elements for different directions of light polarization and different directions of the initial-state in-plane wave vector, including low-symmetry directions. We trace how the optical matrix elements and absorption are modified when spin-orbit interaction and important symmetry breaking mechanisms are taken into account (structural inversion asymmetry, bulk inversion asymmetry, and interface Hamiltonian). These mechanisms result in an almost 100% anisotropy of the absorption coefficients as the light polarization vector rotates in the plane of the structure and in a plane normal to the interfaces.     

Simulation of the vector wave field of a low-frequency sound source in the ocean: Some important features

An approach to the simulation of low frequency vector wave fields in stratified media (mainly in the ocean) is considered. The approach is characterized by an improved stability with respect to dividing the medium into many layers of arbitrary thickness. The model for the sound field of a point source is based on an integral representation of two-dimensional, cylindrically symmetric vector wave fields in inhomogeneous media, so that the contributions of all types of waves are included automatically. The model medium is subdivided into N horizontally homogeneous layers for which 4(N?1) equations are formulated to satisfy the boundary conditions between adjacent layers. The method of the generalized Schmidt matrix is used to obtain the coefficients of the equations; these coefficients are substituted into the expressions (of the Fourier-Bessel integral type) for the local parameters of the field. The latter are calculated according to the numerical procedure, and the results are used to model the distributions of the acoustic pressure and the horizontal and vertical components of the particle velocity in liquid and elastic media. The instability of the calculation procedure may result in a disagreement between the model and the exact solution. However, the disagreement is shown to occur mainly in models containing excessively thick layers. A way for improving the stability of the numerical model is suggested. The simulation results are compared with the exact analytical solution for the simplest example and with the results obtained according to the commonly used generalized matrix procedure (the benchmark problem). The examples of the practical application of the model for investigating more complex seismoacoustic wave fields in the ocean are presented.     

Solitary Wave Solutions of a Generalized Derivative Nonlinear Schrödinger Equation

With the aid of a class of nonlinear ordinary differential equation (ODE) and its various positive solutions, four types of exact solutions of the generalized derivative nonlinear Schrödinger equation (GDNLSE) have been found out, which are the bell-type solitary wave solution, the algebraic solitary wave solution, the kink-type solitary wave solution and the sinusoidal traveling wave solution, provided that the coefficients of GDNLSE satisfy certain constraint conditions. For more general GDNLSE, the similar results are also given.     

On the characterization of vector rogue waves in two-dimensional two coupled nonlinear Schrödinger equations with distributed coefficients

We construct vector rogue wave solutions of the two-dimensional two coupled nonlinear Schrödinger equations with distributed coefficients, namely diffraction, nonlinearity and gain parameters through similarity transformation technique. We transform the two-dimensional two coupled variable coefficients nonlinear Schrödinger equations into Manakov equation with a constraint that connects diffraction and gain parameters with nonlinearity parameter. We investigate the characteristics of the constructed vector rogue wave solutions with four different forms of diffraction parameters. We report some interesting patterns that occur in the rogue wave structures. Further, we construct vector dark rogue wave solutions of the two-dimensional two coupled nonlinear Schrödinger equations with distributed coefficients and report some novel characteristics that we observe in the vector dark rogue wave solutions.     

水平极化光在单轴吸收晶体中的传播

根据光在各向同性吸收介质中传播的分析方法,引入了波法线矢量传播常量,讨论了水平极化光在单轴吸收晶体中的传播规律,得到了波法线折射率、光线折射率、吸收系数等描述吸收晶体性质和光传播性质的物理量的表达式,推导出透明晶体的相应公式.数值计算表明,由该法得到的晶体表面的反射和透射系数与用复折射率表示法得到的结论一致.     

Compression induced folding of a sheet: an integrable system

The apparently intractable shape of a fold in a compressed elastic film lying on a fluid substrate is found to have an exact solution. Such systems buckle at a nonzero wave vector set by the bending stiffness of the film and the weight of the substrate fluid. Our solution describes the entire progression from a weakly displaced sinusoidal buckling to a single large fold that contacts itself. The pressure decrease is exactly quadratic in the lateral displacement. We identify a complex wave vector whose magnitude remains invariant with compression.     

Some general properties of the exact acoustic fields in horns and baffles

The propagation of the fundamental, longitudinal acoustic mode in a duct of variable cross-section is considered, and the “Webster” wave equations for the sound pressure and velocity are used to establish some general properties of the exact acoustic fields. The equipartition of kinetic and compression energies is shown (section 2.1) to hold at all stations only for (i) a duct of constant cross-section and (ii) an exponential horn; these are the two cases for which the wave equations for the acoustic velocity and pressure coincide. It is proved (section 2.3) that there are only five duct shapes, forming two dual families, which have constant cut-off frequency(ies): namely, (I) the exponential duct, which is self-dual, and is the only shape with constant (and coincident) cut-offs both for the velocity and pressure; (II) the catenoidal horns, of cross-section S～cosh², sinh², which, with their duals (III) the inverse catenoidal ducts S～sech², csch², have one constant cut-off frequency, respectively, for the acoustic pressure and velocity. The existence of at least one constant cut-off frequency implies that the corresponding wave equation can be transformed into one with constant coefficients, and thus the acoustic fields calculated exactly in terms of elementary (exponential, circular and hyperbolic) functions; this property also applies to the imaginary transformations of the above shapes, viz., the sinusoidal S～sin² and inverse sinusoidal S～csc² ducts, that have no cut-off frequency, i.e., are acoustically “transparent”. It is shown that elementary exact solutions of the Webster equation exist only (section 3.1) for these seven shapes: namely, the exponential, catenoidal, sinusoidal and inverse ducts; it is implied that for all other duct shapes the exact acoustic fields involve special functions, in infinite or finite terms, e.g., Bessel and Hermite functions respectively for power-law and Gaussian horns. Examples of the method of analysis are given by calculating, in elementary form, the exact acoustic fields in inverse catenoidal ducts, for all cases of (a) propagating waves above, (b) non-oscillating modes below and (c) transition fields at the cut-off frequency. The inverse catenoidal ducts consist of (A) the horn of cross-section S～sech², ressembling the “soliton” of non-linear water wave fame, and (B) the baffle of cross-section S～csch², which also matches two exponentially converging ducts, but has infinite, instead of finite, flare at the origin. The geometrical and acoustic properties of these ducts are illustrated by sets of six plots, in Figure 1(a) for the sech-horn and in Figure 1(b) for the csch-baffle; the exact acoustic fields are described by amplitude and phase decompositions of the sound velocity and pressure, plotted as functions of position along the duct, for four frequencies ranging from the cut-off condition to the ray limit (or W.K.B.J. approximation).     

Resonant transition radiation of solar radio bursts

We calculate the resonant transition radiation (RTR) using the most general formulas and obtain approximate analytical expressions describing the RTR dependence on the fast-particle velocity and magnetic-field intensity. Dependence of the RTR on the angle between the wave vector and the magnetic-field direction and also on the thermal velocity of background-plasma electrons is considered on the basis of approximate expressions for RTR, in which the longitudinal dielectric permittivity of the plasma is written neglecting the wave vector of transverse electromagnetic waves. The obtained dependences are combined into unified expressions for RTR coefficients. Comparison with the earlier found RTR coefficients is performed. It is shown that the obtained coefficients correspond better to the nature of the resonant transition radiation. Finally, the obtained RTR coefficients are used for interpretation of the radio emission of the solar burst of December 24, 1991. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 50, No. 5, pp. 371–386, May 2007.     

A neutron diffraction investigation of the sinusoidal atomic displacement wave in pure chromium

A neutron diffraction investigation on a single crystal of chromium, which is approximately single-Q, confirms the existence of a sinusoidal atomic displacement wave in the antiferromagnetic state. The wave is observed to be polarized parallel to the spin density wave (SDW) wavevector, Q, and to have a wavevector 2Q in both the transversely and longitudinally polarized SDW phases. The amplitude of the displacement wave is found to be proportional to the square of the amplitude of the SDW. We obtain for the displacement wave amplitude (0.0017 ± 0.0002)a at 130 K, where a is the lattice parameter.     

The effect of reflectance coefficients on the interaction of an H wave with a thin metal film

The interaction between an H wave and a thin metal film is calculated in the case of different values of the angle of incidence θ of the wave and reflectance coefficients q ₁ and q ₂ upon reflection of electrons from the surface of a thin metal layer. The behavior of the reflection, transmission, and absorption coefficients is analyzed as a function of the dimensionless frequency of bulk collisions of electrons X and dimensionless frequency of the external field y. The obtained results are compared with experimental data.     

Anomalous resistivity near Néel temperature due to the critical scattering: Antifferomagnet

Critical behaviour of the temperature derivative of the electrical resistivity at the Néel temperature is treated. For a small Fermi wave vector, the divergence is the same as that of the specific heat both above and below the Néel temperature. For a large Fermi wave vector, in paramagnetic region, the contributions from the critical and the other regions of q-space are of the same divergence as the specific heat but of different signs from each other. Below Néel temperature, the gap effect is the main origin of divergence.     

Single bubble sonoluminescence driven by non-simple-harmonic ultrasounds

The dependence of the single bubble sonoluminescence (SBSL) on the waveforms of the driving ultrasound has been investigated by both experiment and numerical calculation. Three types of non-simple-harmonic waves, the rectangular, triangular and as well as the sinusoidal wave with a pulse, are used to drive the SBSL in our research. The triangular wave is the most effective, while the rectangular wave is the worst and the sinusoidal wave in the middle. However, the rectangular wave drives the brightest SBSL among those waves if the sound pressure amplitude keeps constant. When we use a simple-harmonic wave with a pulse as the driving sound, stable and periodic SBSL flashes have been observed. An increase in the flash intensity can be observed as the pulse is put at a suitable phase related to the sinusoidal wave. All of the observations are investigated numerically. Well qualitative agreements between the numerical simulations and the experimental measurements have been achieved.     

Solutions of scalar and electromagnetic wave equations in the metric of gravitational and electromagnetic waves

The wave equation for a scalar field ? and vector potentialA* are solved in the background metric of a gravitational wave. The corresponding solutions when the metric is generated by a plane electromagnetic wave, is obtained from these solutions. The solution for the scalar wave is discussed in detail. It is found that because of the interaction, two new waves are generated in the lower order approximations. One of them has the same phase dependence as the original wave while the other shows a transient character. There is no interaction when the waves are along the same direction.     

Acoustic scattering of a high-order Bessel beam by an elastic sphere

The exact analytical solution for the scattering of a generalized (or “hollow”) acoustic Bessel beam in water by an elastic sphere centered on the beam is presented. The far-field acoustic scattering field is expressed as a partial wave series involving the scattering angle relative to the beam axis and the half-conical angle of the wave vector components of the generalized Bessel beam. The sphere is assumed to have isotropic elastic material properties so that the nth partial wave amplitude for plane wave scattering is proportional to a known partial-wave coefficient. The transverse acoustic scattering field is investigated versus the dimensionless parameter ka(k is the wave vector, a radius of the sphere) as well as the polar angle θ for a specific dimensionless frequency and half-cone angle β. For higher-order generalized beams, the acoustic scattering vanishes in the backward (θ = π) and forward (θ = 0) directions along the beam axis. Moreover it is possible to suppress the excitation of certain resonances of an elastic sphere by appropriate selection of the generalized Bessel beam parameters.     

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.