Chaotic scattering and acceleration of particles by waves

Relativistic charged particles in a uniform magnetic field and traveling waves of large amplitude can be accelerated limitlessly. Since much of phase space is chaotic the process can be viewed as chaotic scattering on waves. For multiple waves an explicit map arises with unusual properties. It contains infinite island chains around nonperiodic orbits and it is also an example of transient chaos in a Hamiltonian system.     

Attenuation of phonon scattering intensities by point defects

The cross section of the coherent, inelastic neutron scattering is characteristically decreased in the presence of defect-induced lattice distortions. This effect is in analogy to the attenuation of Bragg intensities due to a static Debye-Waller factor. The integrated scattering intensities from transversal acoustic (TA-) phonons of the system NbN_0.014 have been measured and are shown to be attenuated with respect to the scattering intensities from the phonons of a pure Nb crystal. We discuss the obtained results through comparison with various model calculations.     

Static electric conductivity for scattering by point defects

The problem of interactions with a periodic lattice potential with scattering by a delta-shaped potential is investigated. Using a closed formal expression for the electric conductivity and factorization of the scattering potential, the temperature dependence of the mobility is obtained, over and beyond the results following from the kinetic equation.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 34–45, June, 1987.     

Properties of elastic waves in quasiregular structures with planar defects

We have studied the elastic waves in quasiregular structures following the Fibonacci and Rudin–Shapiro sequences, and having planar defects, that is breaks of the quasiregular structure in different parts of the system. It is seen that the different kinds of defects produce effects on different ranges of the frequency spectrum, and can introduce more localized states in the gaps, or modify the frequencies of the states in the gaps. We have also studied the phase time and transmission coefficients, thus seeing how these localized modes can be used as frequency filters.     

Elastic scattering of acoustic phonons on point mass defects

The relaxation of homogeneous states of long-wave acoustic phonon gas scattered by point mass defects in transversely—isotropic media is studied. The spectrum of the suitable collision operator of the Boltzmann-Peierls equation is investigated. It consists of a continuous part and several discrete eigenvalues. Both continuous and discrete part of the spectrum depend on the values of components of the elastic constant tensor. For some values of elastic constants the continuous part splits up into two separate intervals and some of the discrete eigenvalues appear in the gap. The number of discrete eigenvalues and their arrangement are also affected by elastic properties of medium.     

Elastic scattering of acoustic phonons on point mass defects

The problem of eigenvalues of the collision operator for a gas of acoustic phonons scattered by point mass defects of small concentration embedded in transversely isotropic media is considered. For this purpose the properties of solution of the Boltzmann-Peierls kinetic equation for spatially homogeneous states are studied. An analytic formula for the Laplace transform of the distribution function is obtained. The singularities of this Laplace transform and the initial distribution function determine the dependence of this distribution function on time. For several hexagonal materials characteristics of the singularity set are calculated. Usually the singularity set consists of a continuous part and four discrete points. However, there exist elastic hexagonal materials (⁴He, Cd, Ta, Zn) for which some of discrete points are absent. For some materials (e.g. Zr) the continuous part is very narrow.     

Temperature dependence of mobility in scattering on point defects

Scattering amplitude in the field of a short-range force center is calculated using factorization of the potential. The results obtained are used to study the temperature dependence of charge-carrier mobility in the random field of chaotically distributed structural point defects.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 50–57, September, 1985.In conclusion, the author sincerely thanks V. L. Bonch-Burevich for his interest in the study and most valuable discussions.     

Analysis of point defects in polycrystalline BaTiO3 by electron paramagnetic resonance

Several paramagnetic point defects in BaTiO₃ polycrystals were detected and identified using the electron paramagnetic resonance technique. Polycrystalline samples sintered in a reducing atmosphere showed a broad signal with a giromagnetic constant of 1.932. This signal, observed only in conducting ceramics, was assigned to Ti³⁺ and its related complexes. V_Ba and V_Ti defects were found at giromagetic constants of 1.974 and 2.004, respectively. The EPR intensity of these defects increases after oxidising at T>1000 °C. The appearance of the V_Ba and V_Ti signals in EPR spectra of oxidized ceramics correlates with the onset of the PTCR effect. At donor dopant levels ≥0.3 at.%, the concentration of V_Ba and V_Ti shows good agreement with the defect compensation mechanism of donor doped BaTiO₃. However, small amounts of V_Ba and V_Ti were also detected in undoped BaTiO₃, contrary to the generally accepted defect model.     

Broadening of paramagnetic resonance lines by charged point defects in neodymium-doped scheelites

We study paramagnetic resonance linewidth in a series of CaWO₄ and CaMoO₄ crystals with different concentrations of neodymium ions (0.0031–0.81 at %). Experimental data are interpreted in the framework of the statistical theory of line broadening by charged point defects. In our calculations, three different contributions are singled out: arising from the local electric fields, electric field gradients and magnetic fields of the nearby point defects. The interaction parameters are determined from the spectroscopic data available for Nd:CaWO₄ crystal. Direct calculations of the linewidth are performed for different crystal orientations with respect to external magnetic field. We conclude that major contribution to the broadening comes from the interactions with random electric fields produced by neodymium and charge compensator ions.     

利用电子顺磁共振研究介电陶瓷的杂质及点缺陷

采用电子顺磁共振(EPR)技术研究了基于钛酸钡的介电陶瓷材料中的杂质及点缺陷.伴随温度的结构相变,概括了由杂质和点缺陷所诱致的EPR信号对于一级相变和扩散相变的特征.     

Multiple scattering of short waves in a system of interacting particles

The multiple scattering of a plane wave in a system of scatterers (a nonideal gas) is examined for certain constraints on the wavelength and interaction potential. For the ideal gas model, the radiation intensity is described by the kinetic transport equation. An analogous equation is obtained which accounts exactly for the pair collisions of the scatterers, and approximately for higher-order collisions.In conclusion, the author wishes to express his appreciation for valuable discussions with V. E. Zuev and S. D. Tvorogov.     

Multiple scattering of short waves at a system of interacting particles

A plane wave incident on a classical nonideal gas is considered. The mean field is derived up to terms for pair collisions of the scattering particles subject to certain assumptions about the wavelength and the interaction potential.I am indebted to V. E. Zuev and S. D. Tvorogov for many discussions.     

On the theory of multiple scattering of sound waves by spherical particles in liquid and elastic media

Two independent systems of equations are derived for describing the scalar and vector potentials of the sound field in a liquid or elastic medium containing discrete inhomogeneities. One of the systems determines the sound field as the sum of the fields scattered by the particles according to the law of scattering by a single particle with the oscillation amplitudes governed by the properties of the inhomogeneous medium. The other system determines the sound field as the sum of the scattered fields formed in the inhomogeneous medium with the oscillation amplitudes of a particle in a homogeneous medium. Expressions relating the fields that occur in a medium consisting of N particles to the fields in a medium consisting of N − 1 particles are proposed. These expressions may simplify and diversify the methods used for computer simulation of sound fields with the aim to verify the calculations. The results of the study are valid for any particle concentrations under the condition that the scattering by a single particle is determined by its monopole, dipole, and rotary oscillations.     

Phonon scattering by paraelastic defects

The relaxation timeτ(ω) for the scattering of the lattice waves of frequencyω by the paraelastic defects has been calculated by using the Feynman graph method, applied to a previous theoretical model [8]. A simple expression for the resonance component ofτ(ω)⁻¹ has been derived.

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Zusammenfassung Die Relaxationszeitτ(ω) für die Streuung der Gitterwellen der Frequenzω an den paraelastischen Defekten wurde nach der Methode der Feynmanschen Graphen berechnet, wobei ein früheres theoretisches Modell [8] angewendet wurde. Ein einfacher Ausdruck für den Resonanzteil vonτ(ω)⁻¹ wurde hergeleitet.

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Résumé Nous avons calculé le temps de relaxationτ(ω) des ondes du réseau de fréquenceω, qui sont diffusées par des défauts para-élastiques, en appliquant la méthode des graphes de Feynman à un modèle théorique antérieur [8]. Une simple expression pour la partie résonante deτ(ω)⁻¹ a été dérivée.

     

Electron paramagnetic resonance study of impurities and point defects in oxide crystals

In this topic review the results of the X-band electron paramagnetic resonance (EPR) measurements of Mn, Co, Cr, Fe ions in YAlO₃ (YAP) crystals and Fe ions in LiNbO₃ (LNO) crystals and of chromium doped Bi₁₂GeO₂₀ (BGO) and Ca₄GdO(BO₃)₃ single crystals, are presented. It is well known that the oxide crystals (for example:YAP, LNO, BGO) are one of the most widely used host materials for different optoelectronic applications. The nature of point defect of impurities and produced in the oxide crystal after irradiation by bismuth ions and after irradiation by the ²³⁵U ions with energy 9.47 MeV/u and fluency 5?×?10¹¹?cm^?1 is discussed. The latter is important for applications of these oxide crystal as laser materials.     

The scattering and transmission of elastic waves in quasi-two-dimensional planar waveguides with linear defect boundaries

The influence of linear defect boundaries on the transmission and scattering of elastic waves in quasi-two-dimensional wave-guides is studied using the matching method. A linear defect boundary separating two wave-guide crystalline lattice domains is characterised here by a linear chain of defect masses and by modified elastic constants in the boundary, different from their values in the bulk of the domains. In particular a square lattice is considered to model the domains of the two-dimensional planar wave-guide containing the linear defect. The reflection and transmission probabilities, and the total transmission probabilities are calculated numerically and presented for the scattering processes in a variety of cases. We show that the interaction between the localised modes introduced by the defect boundary and the propagating modes of the system leads to Fano resonances. These resonances shift to higher (lower) frequencies for smaller (larger) defect masses, and for the same mass as function of the angle of the incident wave. Other spectral features shown to exist are due to interference effects especially at oblique incidence and when modifying the boundary elastic constants. Received 8 November 1999 and Received in final form 14 January 2000