Novel effects of electron-phonon interaction in quasi-two-dimensional structures located in a magnetic field

This paper studies the interaction of electrons and acoustic phonons in a quasi-two-dimensional system with an asymmetric quantizing potential in a magnetic field that is parallel to the structure’s plane. It is demonstrated that the electron-phonon interaction in such a system generates an emf when there is a standing acoustic wave, as well as when the structure is heated uniformly. These phenomena are macroscopic manifestations of a universal quantum effect, which amounts to an emf being generated by any isotropic perturbation of any electron system in which the energy depends asymmetrically on the velocity υ, i.e., ε(υ)≠ε(−υ). Zh. éksp. Teor. Fiz. 115, 959–969 (March 1999)     

Sound attenuation in a random waveguide when using a radiating system with different patterns of directivity

Using numerical simulations of sound propagation on Russia’s shallow Arctic shelf, low frequency sound attenuation is analyzed for acoustic sources with different patterns of directivity, i.e., vertical discrete radiating arrays of different length. It is shown that sound attenuation depends largely on the parameters of patterns of directivity and the intensity of surface waves even at short ranges r from a source (r < 250H, where H is the waveguide depth).     

Differential approximation for Kelvin wave turbulence

I present a nonlinear differential equation model (DAM) for the spectrum of Kelvin waves on a thin vortex filament. This model preserves the original scaling of the six-wave kinetic equation, its direct and inverse cascade solutions, as well as the thermodynamic equilibrium spectra. Further, I extend DAM to include the effect of sound radiation by Kelvin waves. I show that, because of the phonon radiation, the turbulence spectrum ends at a maximum frequency of ω* ∼ (ε³ c _s ²⁰ /κ¹⁶)^1/13, where ε is the total energy injection rate, c _s is the speed of sound, and κ is the quantum of circulation. The text was submitted by the author in English.     

Confinement of massless particles: Photon

Confinement of massless particles in a suitably chosen dielectric medium is considered. Light waves of selected frequencies are shown to be confined in a medium with dielectric constantε(r)=a/r−b ². A wave theoretical analysis gives equispaced frequency spectrum for the confined light, the radial dependence of its electric wave vector resembling that of hydrogen atom wave functions. In the large frequency limit an eikonal approximation of the problem gives elliptic orbits for the confined rays. Higher frequency orbits are shown to be closer to the centre of the medium than the lower frequency ones.     

Some New Results for McKean’s Graphs with Applications to Kac’s Equation

The main goal of the present paper is to sharpen some results about the error made when the Wild sums, used to represent the solution of the Kac analog of Boltzmann’s equation, are truncated at the n-th stage. More precisely, in Carlen, Carvalho and Gabetta (J. Funct. Anal. 220: 362–387 (2005)), one finds a bound for the above-mentioned error which depends on (an ^Λ+ε). On the one hand, it is shown that Λ, the least negative eigenvalue of the linearized collision operator, is the best possible exponent. On the other hand, ε is an extra strictly positive number and a a positive coefficient which depends on ε too. Thus, it is interesting to check whether ε can be removed from the above bound. According to the aforesaid reference, this problem is studied here by means of the probability distribution of the depth of a leaf in a McKean random tree. In fact, an accurate study of the probability generating function of such a depth leads to conclude that the above bound can be replaced with (a′ n ^Λ).     

Excitation of the acoustic and leaky waves in the atmosphere by a sub-surface seismic source

We study excitation of acoustic, leaky, and surface waves by a time-harmonic force source located in a homogeneous isotropic elastic half-space contacting a homogeneous gas. The force acts in the normal direction to the interface between the media. We consider the case where the sound velocity in the gas is less than the velocity of the Rayleigh wave propagating along the surface of the solid. An expression is derived for the period-averaged radiation power of the surface Stoneley wave. The total radiation power is calculated for the acoustic wave in the gas and for the leaky pseudo-Rayleigh wave. Variations in the radiation powers of the surface and leaky waves are analyzed as functions of the source depth. If the velocities of compressional and shear waves in the elastic medium significantly exceed the sound velocity in the gas, then the radiation power of the Stoneley wave turns out to be a factor of 10⁶–10⁸ smaller than the radiation powers of other waves. The radiation power of the Stoneley wave decreases monotonically with increasing source depth, and the decrease becomes more pronounced with the increase in the difference between the acoustic impedances of the contacting media. If the shear-wave velocity in the solid is close to the sound velocity in the gas, then the radiation power of the Stoneley wave is comparable with the radiation powers of other waves and exhibits maximum at a certain source depth. For some parameters of the gas and the solid, and for certain source depths, the Stoneley wave carries away more than a half of the total radiation power. It is shown that, for certain relations between the parameters of the media, the radiation power of the Stoneley wave increases due to redistribution of the radiated power from the pseudo-Rayleigh leaky wave. The total power of these waves remains approximatly constant and, with accuracy of the order of 10⁻³, is equal to the radiation power of the Rayleigh wave at the vacuum-solid interface. It is shown that the acoustic-wave power which can be transmitted to the upper layers of the atmosphere during an earthquake does not exceed 0.01% of the total power radiated at a given frequency. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 49, No. 7, pp. 577–592, July 2006.     

The dynamical mixing of light and pseudoscalar fields

We solve the general problem of mixing of electromagnetic and scalar or pseudoscalar fields coupled by axion-type interactions L _int = g _ϕ ϕε _μναβ F ^μν F ^αβ . The problem depends on several dimensionful scales, including the magnitude and direction of background magnetic field, the pseudoscalar mass, plasma frequency, propagation frequency, wave number, and finally the pseudoscalar coupling. We apply the results to the first consistent calculations of the mixing of light propagating in a background magnetic field of varying directions, which show a great variety of fascinating resonant and polarization effects.      

Mechanism of stratification of turbulent heat transfer in a sound field in the presence of rotational anisotropy of the flow

It is established that the stratification of the heat transfer intensity coefficients into n discrete levels, as discovered previously in the turbulent flow accompanying rotation of a supersonic flow, is described by the formula α _n ² /α ₁ ² =2 ⁿ⁻¹, n=1,2,3,.... It is found that the ratio of the measured amplitudes of the discrete components of the pressure-pulsation spectrum is of a similar form and corresponds to the pressure field from multipole sources. As expected, similarly to the case of acoustic paramagnetic resonance, the selection of discrete frequencies of intense acoustic radiation from the external flow occurs under the influence of resonances with the radiation of multipoles of turbulent vortices oriented in the rotational anisotropy field. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 2, 145–149 (25 January 1997)     

Nonlinear acoustoelectronic interaction in thin superconducting lead films

The effect of high-power surface acoustic waves (SAW) on the superconducting state of Pb films has been studied in different transverse magnetic fields. It was established that a high-intensity sound wave affects the T _c of the film and the character of the superconducting transition, and that the observed changes are the larger, the higher is the SAW intensity. It was found that high-power SAW are capable of inducing vortex depinning in the film and reducing the critical current. Various mechanisms which are responsible for the nature of these effects are discussed. Fiz. Tverd. Tela (St. Petersburg) 39, 1753–1760 (October 1997)     

Sound Attenuation in a Circular Duct of a Viscous Medium in the Absence of Mean Flow

Abstract

An analytical method to study the effect of viscosity of a medium and the wave number on sound propagation and sound attenuation numbers in circular ducts has been presented. The method is based on the variation of parameters of the solution corresponding to the case of inviscid acoustic waves in circular ducts and axisymmetric modes. A mathematical model is constructed to describe the physical problem in general. Three basic assumptions have been considered, namely, each flow quantity has been written as the sum of a steady mean flow and an unsteady acoustic flow quantity. The effect of thermal conductivity of the gas has been neglected as well as no mean flow. The results for a wide range of wave numbers and Reynolds numbers show that for a viscous medium, the propagation number is a weak function of the Reynolds number, and as the Reynolds number increases, the propagation number approaches its inviscid value. Also the propagation number is independent of the wave number. For the attenuation number, it decreases monotonically with the increase of the Reynolds number and it vanishes when Reynolds number exceeds 10⁴.     

On the electric activity of superfluid helium at the excitation of first and second sound waves

We show that the electric activity of superfluid helium (HeII) observed in the experiments [3] during the excitation of standing second sound waves in an acoustic resonator can be described in terms of the phenomenological mechanism of the inertial polarization of atoms in a dielectric, in particular, in HeII, when the polarization field induced in the medium is proportional to the mechanical acceleration, by analogy with the Stewart-Tolman effect. The variable relative velocity w = v _n − v _s of the normal and superfluid HeII components that emerges in the second sound wave determines the mean group velocity of rotons, V _g ≈ w, with the density of the normal component related to their equilibrium number density in the temperature range 1.3 K ≤ T ≤ 2 K. Therefore, the acceleration of the 4He atoms involved in the formation of a roton excitation is proportional to the time derivative of the relative velocity.w. In this case, the linear local relations between the variable values of the electric induction, electric field strength, and polarization vector should be taken into account. As a result, the variable displacement current induced in the bulk of HeII and the corresponding potential difference do not depend on the anomalously low polarizability of liquid helium. This allows the ratio of the amplitudes of the temperature and potential oscillations in the second sound wave, which is almost independent of T in the above temperature range, consistent with experimental data to be obtained. At the same time, the absence of an electric response during the excitation of first sound waves in the linear regime is related to an insufficient power of the sound oscillations. Based on the experimental data on the excitation of first and second sounds, we have obtained estimates for the phenomenological coefficient of proportionality between the polarization vector and acceleration and for the drag coefficient of helium atoms by rotons in the second sound wave. We also show that the presence of a steady heat flow in HeII with nonzero longitudinal velocity and temperature gradients due to finite viscosity and thermal conductivity of the normal component leads to a change in the phase velocities of the first and second sound waves and to an exponential growth of their amplitudes with time, which should cause the amplitudes of the electric signals at the first and second sound frequencies to grow. This instability is analogous to the growth of the amplitude of long gravity waves on a shallow-water surface that propagate in the direction of decreasing basin depth.     

Stimulated scattering and wavefront conjugation in an inhomogeneous plasma

In the context of the problem of stimulated scattering we discuss the mechanism of wavefront conjugation in an inhomogeneous plasma proposed relatively recently, associated with a difference in suppression of scattering (due to inhomogeneities) for the inverted and uninverted components. We analyze the solutions of the integro-differential equations describing this process both numerically and analytically for different sound attenuation lengths (v ⁻¹). It is shown that for this effect to exist it is necessary that n not be too small. We also consider extinction of the inverted wave in terms of this mechanism. Zh. éksp. Teor. Fiz. 113, 168–180 (January 1998)     

Four-magnon decay of magnetostatic surface waves in yttrium iron garnet films

The four-magnon instability of magnetostatic surface waves (MSSWs) in yttrium iron garnet epitaxial films is investigated experimentally. It is shown that four-magnon instability for MSSWs with wave numbers 30–600 cm⁻¹ is a decay instability and develops for values of the wave magnetization close to the threshold level for second-order parametric instability of a homogeneous transverse pump wave. When the supercriticality of the MSSW power is 15–20 dB, the generated parametric spin waves themselves become unstable with respect to the four-magnon interaction, so that kinetic instability develops in the film. It is shown that the pump signal transmitted through the signal and the length of the “nonlinear” part of the film, where a MSSW is capable of exciting parametric spin waves, increase as the pump power is increased. Fiz. Tverd. Tela (St. Petersburg) 38, 330–338 (February 1997)     

Nonlinear dynamics of vortices pinned to unidirectional twins

The nonlinear resistive properties of superconductors in the mixed state in the presence of a system of unidirectional planar defects (twins) have been investigated theoretically within the framework of the two-dimensional stochastic model of anisotropic pinning based on the Fokker-Planck equations with a concrete form of the pinning potential. These equations allow one to obtain an exact analytical solution of the problem. Formulas are obtained for experimentally observable even and odd (relative to reversal of the direction of the external magnetic field) nonlinear longitudinal and transverse magnetoresistivities ρ _‖,⊥ ^± ( j,t,α,ε) as functions of the transport current density j, temperature t, the angle α between the directions of the current and the twins, and the relative volume fraction ε occupied by the twins. In light of the great variety of types of nonlinear resistive dependences contained in these expressions for ρ _‖,⊥ ^± the most characteristic of them are presented in the form of graphs with commentary. The desired nonlinear dependences ρ _‖,⊥ ^± are linear combinations of the even and odd parts of the function v(j,t, α,ε), which has the sense of the probability of overcoming the potential barrier of the twins; this makes it possible to give a simple physical treatment of the nonlinear regimes. New scaling relations for the Hall conductivity are obtained and investigated which differ from the previously known relations for isotropic pinning. The interaction of vortex motion directed along the twins and the Hall effect is considered for Hall constants which are arbitrary in magnitude and sign, and it is shown that in the case of small Hall viscosity vortex motion directed along the twins has an effect on the odd magnetoresistivities ρ _‖ ⁻ and ρ _⊥ ⁻ , whereas the reverse effect can be neglected. It is shown that pinning anisotropy is sufficient to manifest the new nonlinear (in the current) magnetoresistivities ρ _⊥ ⁺ and ρ _‖ ⁻ . Zh. éksp. Teor. Fiz. 116, 2103–2129 (December 1999)     

Frequency shifts of the sound field interference pattern on oceanic shelf in summer conditions

Considerable shifts Δf/ϕ ≈ 10⁻¹ of the low-frequency sound field interference pattern in the frequency domain, associated with barotropic tide and internal tidal waves, were observed in the Shallow Water’06 experiment on the New Jersey shelf in the summer of 2006. The acoustic frequency shifts appear to be strongly dependent on the modes of the sound field. By examining different modal structure, it is possible to analyze the overall interference pattern and find which part is more sensitive either to the surface tide or the internal waves. This feature can be exploited to acoustically monitor tidal waves of different kinds.     

Acoustic analog of the Fermi resonance

It is shown that for acoustic waves in crystals nonlinear phenomena of a new type, analogous to some degree to Fermi resonance in molecules, can occur. It is demonstrated on the basis of an analysis of the numerical solution of the equations of motion that for propagation of waves with different polarization and with sound velocities in integral ratio, the energy transfer from one wave to another is of the nature of beats with quite low amplitudes and can become chaotic as the amplitudes increase. Pis’ma Zh. éksp. Teor. Fiz. 69, No. 6, 417–422 (25 March 1999)     

Interaction of second sound with acoustic waves in solids

An expression has been derived for the collision operator for phonons in a solid, which is valid at very low temperatures. The set of coupled equations for the elastic deformation and the phonon density or second sound has been reduced to a simple tractable form and the dispersion equation for the coupled waves consisting of the acoustic modes and second sound has been derived. It is shown that only the longitudinal mode interacts with the second sound. It is also shown that as a result of the interaction with the second sound, the longitudinal velocity along the principal axis acquires a correction term that is proportional to bothγ ² andT ⁴. The author felicitates Prof. D S Kothari on his eightieth birthday and dedicates this paper to him on this occasion.     

Microscopic three-cluster study of the low-energy 9 Be photodisintegration

The ⁹Be and ⁹B nuclei are investigated in a microscopic three-cluster model involving α + α + n (or α + α + p) configurations. The ⁸Be (0 ⁺ , 2 ⁺ ) + n and ⁵He (3/2 ^- , 1/2 ^- ) + α (or mirror) channels are included by taking account of the unstable nature of ⁸Be and ⁵He. Spectroscopic properties of ⁹Be and ⁹B are analyzed. We show that the ⁵He + α configurations cannot be neglected to derive accurate results. The ⁹Be(γ,αα)n photodisintegration cross-section is shown to be mainly determined by ⁸Be + n channels at low energies, but ⁵He + α channels become important beyond E _γ≈ 4 MeV. Received: 7 September 2001 / Accepted: 19 November 2001     

Distribution of Particles Which Produces a “Smart” Material

If A _q(β, α, k) is the scattering amplitude, corresponding to a potential , where D⊂ℝ³ is a bounded domain, and is the incident plane wave, then we call the radiation pattern the function , where the unit vector α, the incident direction, is fixed, β is the unit vector in the direction of the scattered wave, and k>0, the wavenumber, is fixed. It is shown that any function , where S ² is the unit sphere in ℝ³, can be approximated with any desired accuracy by a radiation pattern: , where ∊ >0 is an arbitrary small fixed number. The potential q, corresponding to A(β), depends on f and ∊, and can be calculated analytically. There is a one-to-one correspondence between the above potential and the density of the number of small acoustically soft particles D _m⊂ D, 1≤ m≤ M, distributed in an a priori given bounded domain D⊂ℝ³. The geometrical shape of a small particle D _m is arbitrary, the boundary S _m of D _m is Lipschitz uniformly with respect to m. The wave number k and the direction α of the incident upon D plane wave are fixed. It is shown that a suitable distribution of the above particles in D can produce the scattering amplitude , at a fixed k>0, arbitrarily close in the norm of L ²(S ²× S ²) to an arbitrary given scattering amplitude f(α ', α), corresponding to a real-valued potential q∊ L ²(D), i.e., corresponding to an arbitrary refraction coefficient in D. MSC: 35J05, 35J10, 70F10, 74J25, 81U40, 81V05, 35R30. PACS: 03.04.Kf.