Interaction of optical phonons with anisotropic imperfections

Inelastic (Raman) light scattering by phonons interacting with anisotropic imperfections is investigated. Three different kind of disorder-induced defects (point, linear and planar) have been considered. The optical phonon width and line shape are found to depend importantly on the dimension of the imperfections. There is a close correspondence between the scale of the imperfection and the phonon line shape observed in the Raman scattering experiments. The dependence of the phonon frequency shift and width on the defect concentrations is calculated, and the critical concentrations at which the optical phonon can no longer be observed are determined. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 12, 817–822 (25 December 1997) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Extension of the local curvature approximation to third order and improved tilt invariance

The second-order local curvature approximation (LCA2) is a theory of rough surface scattering that reproduces fundamental low and high frequency limits in a tilted frame of reference. Although the existing LCA2 model provides agreement with the first order small perturbation method up to the first order in surface tilt, results reported in this paper produce a new formulation of the model that achieves consistency with perturbation theory to first order in surface height and arbitrary order in surface tilt. In addition, extension of the modified LCA to third order is presented, and allows the theory to match the second-order small perturbation method to arbitrary order in surface tilt. Crucial to the development of the theory are a set of identities involving relationships among the small perturbation method (i.e. low frequency) and Kirchhoff approximation (i.e. high frequency) kernels; a set of new identities obtained in our derivations is also presented. Sample results involving 3D electromagnetic scattering from penetrable rough surfaces, as well as 2D scattering from Dirichlet sinusoidal gratings, are provided to compare the new results with the existing LCA2 model and with other rough surface scattering theories.     

Electric-field influence on the neutron diffuse scattering near the ferroelectric transition of Sr0.61Ba0.39Nb2O6

ABSTRACT

Uniaxial relaxor ferroelectric Sr_0.61Ba_0.39Nb₂O₆ single crystal has been investigated in the vicinity of its phase transition using neutron scattering and dielectric spectroscopy. A global-type thermal hysteresis is evidenced by both techniques in the ferroelectric phase and up to about 15 K above T_c. In addition, a part of the transverse neutron diffuse scattering in the 001 Brillouin zone, presumably related to static nanodomain structure, can be suppressed by prior poling the crystal in electric field of 3 kV/cm. The remaining part of the transverse neutron diffuse scattering and the real part of permittivity show a similar temperature dependence. The temperature position of the maximal scattering intensity T_max depends significantly on the scattering wave vector. T_max shifts monotonically to higher temperature with the increasing wave vector in all investigated cooling and heating regimes. It is concluded that the critical fluctuations have space correlations which depend on frequency and wave vector.     

Anisotropic scattering rates and antiferromagnetic precursor effects in the t-t'-U Hubbard model

We have investigated the evolution of the electronic properties of the t-t'-U Hubbard model with hole doping and temperature. Due to the shape of the Fermi surface, scattering from short wavelength spin fluctuations leads to strongly anisotropic quasi-particle scattering rates at low temperatures near half-filling. As a consequence, significant variations with momenta near the Fermi surface emerge for the spectral functions and the corresponding ARPES signals. At low doping the inverse lifetime of quasiparticles on the Fermi surface is of order varying linearly in temperature from energies of order t down to a very low energy scale set by the spin fluctuation frequency while at intermediate doping a sub-linear T-dependence is observed. This behavior is possibly relevant for the interpretation of photoemission spectra in cuprate superconductors at different hole doping levels. Received 31 July 2000     

Dependence of nuclear diffraction on the azimuthal angle: (002)- and (0010)-reflections of YIG

Nuclear diffraction of synchrotron radiation has been investigated using YIG single crystals in different scattering geometries. Time resolved quantum beat spectra of pure nuclear (002) and (0010) Bragg reflections were observed in a set-up where the hyperfine interaction was kept constant, while the azimuthal angle in the (001) surface between the [100] axis and the scattering plane (k _in,k _out) was varied. The time spectra were analyzed by means of the dynamical theory for coherent nuclear scattering. The results revealed the high sensitivity of this experimental technique on the complete set of hyperfine interaction parameters and on the specific geometrical conditions for nuclear diffraction of polarized γ-rays.     

Universal behaviour of scattering amplitudes for scattering from a plane in an average rough surface for small grazing angles

Abstract

It is shown that for scattering from a plane in an average rough surface, the scattering cross section of the range of small grazing angles of the scattered wave demonstrates a universal behaviour. If the angle of incidence is fixed (in general it should not be small), the diffusive component of the scattering cross section for the Dirichlet problem is proportional to θ² where θ is the (small) angle of elevation, and for the Neumann problem it does not depend on θ. For the backscattering case these dependences correspondingly become θ⁴ and θ°. The result is obtained from the structure of the equations that determine the scattering problem rather than by use of an approximation.     

Analysis of long wavelength electromagnetic scattering by a magnetized cold plasma prolate spheroid

Abstract

Using dielectric permittivity tensor of the magnetized prolate plasma, the scattering of long wavelength electromagnetic waves from the mentioned object is studied. The resonance frequency and differential scattering cross section for the backward scattered waves are presented. Consistency between the resonance frequency in this configuration and results obtained for spherical plasma are investigated. Finally, the effective factors on obtained results such as incident wave polarization, the frequency of the incident wave, the plasma frequency and the cyclotron frequency are analyzed.     

Calculation of the energy density function by the method of steepest descent

We present a unified theory of diatomic molecules which reconciles bound state spectroscopy and atomic scattering theory. The total wave-function is expanded in a complete set of atomic channel states which is entirely equivalent to an expansion in Hund's case (e) electronic-rotational states. An analysis of the coupled radial, that is vibrational, functions places strong constraints on the asymptotic properties of the molecular wave-functions. These are presented in terms of the reactance K and scattering S matrices of atomic scattering theory which offers a uniform treatment for open channels (inelastic scattering and continuum spectroscopy), closed channels (bound state spectroscopy) and mixtures of both (predissociation). The normalization of the total wavefunction is derived and related to the asymptotic boundary conditions both for continuum and bound states.     

Single scattering profile from small-angle scattering data affected by multiple scattering: use of a basis function set

Present work involves extraction of single-scattering profile from small-angle scattering data, affected by multiple scattering, using an existing model-independent algorithm [Mazumder et al., Physica B 241–243, 1222 (1998), Mazumder et al., J. Appl. Crystallogr. 36, 840 (2003)]. It is shown that implementation of the algorithm becomes effective by representing the multiple scattering profiles in terms of a set of basis function whose form of Hankel transformed pair is known analytically. In the present paper, the methodology has been presented by introducing a Gaussian basis set and has been tested for various simulated profiles. The performance of this methodology has also been tested for scattering profiles having complex internal features and moderate statistical noise. Subsequently, the same has been applied for experimental small-angle neutron scattering data.     

Brillouin scattering studies of rare gas solids

Abstract

The scattering of light by elementar excitations in the matter is results in two phenomena, discriminated by the zero wavevector frequency of the excitation: if this frequency is zero, one deals with Brillouin scattering, and with Raman scattering in the other case. Brillouin scattering results from the interaction of light with thermal excitations (acoustic phonons in a crystal) of a material, or, from a classical point of view, with density waves. Contrary to Raman scattering, the selection rules allow always the observation of at least one mode. It is a powerful technic in the study of rare gases under pressure: at ambient temperature, rare gases crystallize in the face centered cubic structure (except helium which structure was recently found to be hexagonal) and are therefore Raman and infrared inactive.

Experimental results will be reviewed on rare gases and rare gas mixtures in the fluid phase, like He-Ne and He-H₂. These results will be discussed in relation with recent measurements of the frequency of global oscillations of Jupiter.     

Optimum structural parameters of fibers in LED-graded index fiber transmission systems

Abstract

The loss in a low-loss multimode optical fiber consists of Rayleigh scattering loss and microbending loss. These losses depend on the structural parameters of the fiber. On the other hand, the coupling optical power from optical source into fiber and connection loss of fibers also depend on the parameters. This paper considers the combination of light emitting diode as an optical source and a graded index fiber as a transmission line and discusses the optimum parameters that give the longest possible span length between an optical transmitter and receiver.     

Exact solution for a degenerate Anderson impurity in the limit embedded into a correlated host

We consider the one-dimensional t - J model, which consists of electrons with spin S on a lattice with nearest neighbor hopping t constrained by the excluded multiple occupancy of the lattice sites and spin-exchange J between neighboring sites. The model is integrable at the supersymmetric point, J = t. Without spoiling the integrability we introduce an Anderson-like impurity of spin S (degenerate Anderson model in the limit), which interacts with the correlated conduction states of the host. The lattice model is defined by the scattering matrices via the Quantum Inverse Scattering Method. We discuss the general form of the interaction Hamiltonian between the impurity and the itinerant electrons on the lattice and explicitly construct it in the continuum limit. The discrete Bethe ansatz equations diagonalizing the host with impurity are derived, and the thermodynamic Bethe ansatz equations are obtained using the string hypothesis for arbitrary band filling as a function of temperature and external magnetic field. The properties of the impurity depend on one coupling parameter related to the Kondo exchange coupling. The impurity can localize up to one itinerant electron and has in general mixed valent properties. Groundstate properties of the impurity, such as the energy, valence, magnetic susceptibility and the specific heat coefficient, are discussed. In the integer valent limit the model reduces to a Coqblin-Schrieffer impurity. Received: 31 December 1997 / Accepted: 17 March 1998     

Stochastically excited waves in a 1D random medium – the mean field and power spectrum

Scalar wave propagation is examined when both the wave source and the propagation speed are random. Results are derived for the mean field and the power spectrum using the second-order Born approximation. The results depend on whether the source S(x, t) and the propagation speed c(x, t) are correlated or not. When they are uncorrelated, the mean field is zero. When they are correlated, the mean field is non-zero only when the source is non-stationary. The power spectrum is incoherent to leading order. There is a transfer of energy from lower to higher frequencies owing to wave scattering. The corresponding frequency upshift of the power profile in the (k, ω) domain is mainly caused by the cross power between the direct and the twice scattered field, which represents a second-order incoherent power contribution. The results are confirmed using a numerical solution of the wave equation where the scattered field is expanded to fifth order.     

Pseudogap-state superconductivity in a “hot-point” model: Gor’kov equations

The specific features of the superconducting state (with s and d pairing) are considered in terms of a pseudogap state caused by short-range order fluctuations of the “dielectric” type, namely, antiferromagnetic (spin density wave) or charge density wave fluctuations, in a model of the Fermi surface with “hot points.” A set of recurrent Gor’kov equations is derived with inclusion of all Feynman diagrams of a perturbation expansion in the interaction between an electron and short-range order fluctuations causing strong scattering near hot points. The influence of nonmagnetic impurities on superconductivity in such a pseudogap state is analyzed. The critical temperature for the superconducting transition is determined, and the effect of the effective pseudogap width, correlation length of short-range-order fluctuations, and impurity scattering frequency on the temperature dependence of the energy gap is investigated.     

Statistics of quantum beats in the time dependence of the neutron scattering

The numerical calculations of the delay time distributions for the neutron scattering have been carried out. The scattering of the short wave packet of neutrons with the broad energy interval 500–800 keV by ⁵⁸Ni nuclei has been studied. The decay curves and average times of the compound scattering were found as for the forward scattering as for the specific spin-parity states. The time oscillations of the decay curves were identified as quantum beats that were caused by the interference of the excited resonance set. The statistical analysis of the frequency spectra of the decay curves oscillations has been carried out. The behavior of the examined statistical observables turns out to be close to the Poisson law.     

Asymmetry of the scattering amplitude of atoms in the field of short counterpropagating light pulses

Rectification in bipotential scattering of a beam of atoms in the field of short pulses of traveling and standing waves is studied: As a result of the coherence induced by the traveling-wave pulse, the momentum transferred to the atomic beam during scattering by the standing wave is nonzero. The magnitude and sign of the asymmetry in the scattering amplitude are oscillatory functions of the duration of the traveling-wave pulse and the detuning of the frequency of the field from atomic resonance. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 12, 920–923 (25 June 1996)     

Distribution of backscattered intensity in the distorted Born approximation: Application to C-band SAR images of woodland

Abstract

The intensity distribution in synthetic aperture radar (SAR) images of woodland is known to depend upon imaging conditions. Whilst phenomenological models can be used to match observed backscatter distributions, a physical model is needed to explain their origins. Images of woodland obtained during airborne SAR trials are analysed and shown to exhibit non-exponential intensity distributions. Expressions are derived for the moments of the intensity distribution using discrete scattering models based on the Born and distorted Born approximations. The predictions of the Born approximation are such that, at all but extremely high resolutions, the intensity statistics reflect only fluctuations in the number of discrete scatterers in resolution cells. In the distorted Born approximation it is revealed that, even at modest resolutions, fluctuations in both number and cross section of objects can influence intensity distributions. This is shown to be a direct consequence of the incorporation of attenuation effects in the distorted Born model. The theory is applied to scattering from a model woodland canopy and shown to yield intensity moments in close agreement with observations. The consequences of the model for other scattering situations are discussed.     

Plasma waves in a nonideal plasma

This paper shows how the concepts commonly used for a Debye plasma—Landau damping, collisional damping, short-range and long-range collisions, and plasma waves—must be revised to describe a nonideal electron-ion plasma. The degrees of freedom of a nonideal plasma are divided into collective and individual. The increase and saturation of the fraction of collective degrees of freedom as the coupling constant increases is discussed. The Tatarskii approach for a system of coupled oscillators makes it possible to model the collective degrees of freedom of a nonideal plasma by a set of Langevin oscillators in a thermostat. The correlation energy and the energy of the plasma waves are found. The concepts developed here made it possible to determine the dispersion of the plasma waves and their damping. The effect of damping on the discrepancy between the position of the maximum of the dynamic structure factor and the real part of the solution of the dispersion equation is considered. The effective collision frequency of the individual degrees of freedom (the electrons) is estimated, taking into account both short-range pairwise scattering and scattering at plasma waves. Zh. éksp. Teor. Fiz. 113, 880–896 (March 1998)     

Integrals of the motion and exact solutions of the problem of two dispersing delta-wells

An exact solution is analyzed for the analogs of bound and scattering states in a nonstationary quantum mechanical system whose potential has the form of two dispersing delta-wells. For the delta-potentials explicit (in the form of operator kernels) expressions are found for the integrals of the motion that depend on time and transform to the known integrals of the motion for a free quantum particle as the interaction force with the potential approaches zero. Zh. éksp. Teor. Fiz. 113, 606–614 (February 1998)