Quantum Cherenkov radiation at the motion of a small neutral particle parallel to the surface of a transparent dielectric

Quantum Cherenkov radiation and quantum friction at the motion of a small neutral particle parallel to the surface of a transparent dielectric with the refractive index n have been studied in a fully relativistic theory. Radiation appears at velocities above the threshold value, v > v _c = c/n. The friction force in the particle–plate configuration has been derived from the friction force in the plate–plate configuration under the assumption that one of the plates is significantly decharged. A decrease in the kinetic energy of the particle near the threshold velocity is due to its radiation and near the speed of light is determined by the heat power absorbed by the particle in the rest frame. The powers of quantum and classical Cherenkov radiation can be comparable in the relativistic case.     

Quantum Cherenkov radiation at the relative sliding of two transparent plates

Quantum Cherenkov radiation and quantum friction at the relative sliding of two transparent plates with the refractive index n have been studied in a fully relativistic theory. Radiation appears at velocities above the threshold value, v > v _c = 2nc/(n ² + 1). The contribution from s-polarized electromagnetic waves dominates near the threshold velocity. However, in the ultrarelativistic case (v → c), contributions from both polarizations are much larger than those in a nonrelativistic theory and a new contribution from the mixing of waves with different polarizations appears. The numerical results are supplemented by analytical calculations near the threshold velocity and the speed of light.     

Nonlinear Raman scattering of photons by a channeled particle

Channeled particles are characterized by the discrete spectrum of bound transverse motion. The interaction of photons with channeled particles in single crystals can be accompanied by energy transitions between the levels of transverse motion of the channeled particle. The Raman scattering of photons at a quasibound channeled particle leads to the appearance of a combination of frequencies: the incident radiation frequency ω₀ and the frequency Δω_{m, n}, i.e., ω = ω₀ ± Δω_m,n where Δω_m,n = 2Δε_m,nγ²; Δε_{m, n} is the energy of the transition between quantum states (m and n) of the transverse motion of the channeled particle; and γ = E/mc² is the Lorentz factor of the channeled particle. The appearance of a violet satellite (the anti-Stokes component) in the Raman scattering spectrum is analyzed. The three-photon Raman-type transition, which is the process of the simultaneous absorption of two photons with the frequency ω₀ with the emission of a photon with the frequency ωs = 2ω₀ ± 2Δε_m,nγ², is considered. The conditions for resonance observation during the formation of the second harmonic (ω = 2ω₀) are discussed.     

Constitutive relations in multidimensional isotropic elasticity and their restrictions to subspaces of lower dimensions

The mechanical meaning and the relationships among material constants in an n-dimensional isotropic elastic medium are discussed. The restrictions of the constitutive relations (Hooke’s law) to subspaces of lower dimension caused by the conditions that an m-dimensional strain state or an m-dimensional stress state (1 ≤ m < n) is realized in the medium. Both the terminology and the general idea of the mathematical construction are chosen by analogy with the case n = 3 and m = 2, which is well known in the classical plane problem of elasticity theory. The quintuples of elastic constants of the same medium that enter both the n-dimensional relations and the relations written out for any m-dimensional restriction are expressed in terms of one another. These expressions in terms of the known constants, for example, of a three-dimensional medium, i.e., the classical elastic constants, enable us to judge the material properties of this medium immersed in a space of larger dimension.     

Maximum coefficient of light extinction in a nonabsorbing dispersive medium

The maximum value of the light extinction coefficient μ, which can be observed in a dispersive medium with a relative refractive index n of the scattering particles, is studied within the framework of a quasi-crystalline approximation for nonabsorbing dispersive media consisting of monodisperse spherical scatterers. A change in the diffraction parameter x of the scattering particles and their volume concentration c _v is accompanied by nonmonotonic variations of the extinction coefficient, and the function μ(x, c _v ) exhibits several maxima. The dimensions and concentrations of particles are determined, for which the extinction coefficient reaches the absolute maximum μ^max. The μ^max value exhibits a monotonic growth with increasing relative refractive index n of the scattering particles. The conditions of validity of the Ioffe-Regel criterion of radiation localization have been studied. It is established that the localization in nonabsorbing dispersive media can be observed only for n ? 2.7. The intervals of x and c _v in which the criterion of radiation localization is satisfied in dispersive media consisting of particles with n = 3.0 and 3.5 are determined.     

Doppler three-level (V-scheme) laser without population inversion

The theory of amplification and lasing without population inversion in a three-level medium with inhomogeneous broadening via the formation of an open V configuration is elaborated. The conditions for energy transfer from the infrared into the visible spectral range, i.e., the conditions of up-conversion n _b >n _c >n _a , and the external field required for saturation of the b?a transition are established. Two-photon resonant Raman transitions in ensemble of mobile atoms of a gas-discharge plasma are analyzed. The frequency shift of the probe field spectrum as a whole is shown to be governed by the frequency shift of the pump field multiplied by the ratio of the wave numbers of the probe amplification field and the pump field. The interaction of atoms through Ne transitions with the pump field (λ=1.15 εm, 2p ₄-2s ₂ transition) and the lasing field (λ=0.6328 εm, 3s ₂-2p ₂ transition) with an increase in the lasing frequency by a factor of 1.82 with respect to the absorbed radiation is calculated.     

Optimization of the Electromagnetic (EM) Perturbative Effects Produced by High-Frequency Gravitational Waves

For the relic gravitational waves in high frequency band, we survey the electromagnetic resonance effect generated from the high frequency gravitational waves, which can be described in the transverse perturbative photon fluxes. Under the fixed tensor-scalar ratio r = 0.2, spectral index n _t = 0 and running index α _t = 0.01, we discuss several properties and quantity changes of the transverse perturbative photon fluxes, which can be improved significantly through setting the longitudinal magnetic component of background EM field in the standard gaussian form, and wave impedance analysis on the transverse direction. Through the theoretical calculation, the transverse perturbative photon fluxes can reach up to 10³ s ^?1 with some optimal parameters such as waist of EM field W ₀ = 0.05m, initial stochastic phase of gravitational waves δ = (0.21 + n)π(n = 0,1,2...). Furthermore the interference of the background transverse photon fluxes can be removed completely through establishing a suitable wave impedance function.     

Evaluation of the dipole interaction of a pair of metal particles in the region of the plasmon resonance

We consider the electric field of an induced dipole moment of a single small particle characterized by the absence of frequency dispersion of the permittivity and the field of a metal particle, which has frequency dispersion and is described in the free electron approximation taking into account the size effects of restriction of the electron free path. The influence of the induced field on the optical properties of a system of small particles is analyzed. It is shown that, for an ensemble of particles without frequency dispersion, the effective medium theory can be used up to concentrations corresponding to filling factors ? ≤ 0.52. In the case of metal particles, with frequency dispersion of dielectric functions and, especially, for the frequency range of the plasmon resonance, this theory can be used only for concentrations not exceeding the threshold ? ≈ 0.01.     

Number of revolutions of a particle around a black hole: Is it infinite or finite?

We consider a particle falling into a rotating black hole. Such a particle makes an infinite number of revolutions n from the viewpoint of a remote observer who uses the Boyer–Lindquist type of coordinates. We examine the behavior of n when it is measured with respect to a local reference frame that also rotates due to dragging effect of spacetime. The crucial point consists here in the observation that for a nonextremal black hole, the leading contributions to n from a particle itself and the reference frame have the same form being in fact universal, so that divergences mutually cancel. As a result, the relative number of revolutions turns out to be finite. For the extremal black hole this is not so, n can be infinite. Different choices of the local reference frame are considered, the results turn out to be the same qualitatively. For illustration, we discuss two explicit examples—rotation in the flat spacetime and in the Kerr metric.     

Features of the energy spectra of photoelectrons at the atomic ionization in a two-color laser field of first and third harmonics

Classical analysis and quantum-mechanical studies of the energy spectra of photoelectrons have been carried out for above-threshold ionization of atoms in a two-color laser field of the first and third (n = 3) harmonics. Numerical computations show that the boundary of direct ionization plateau corresponds to the electron energy E ≈ 3.56 \(U_{p_1 } \), while the boundary of rescattering plateau corresponds to the electron energy E ≈ 16.62 \(U_{p_1 } \) for the two-color field of fundamental frequency and its third harmonic with equal intensities, which is in accordance with the results of classical analysis. The results of classical analysis of the ionization processes in the field of first and nth harmonics of equal intensities show that the length of the direct ionization plateau and the length of the high-energy rescattering plateau decrease with increasing n. The results of numerical analysis of the ionization processes in the field of first and third (n = 3) harmonics correspond to the results of classical analysis carried out by the authors.     

Second-order superintegrable quantum systems

A classical (or quantum) superintegrable system on an n-dimensional Riemannian manifold is an integrable Hamiltonian system with potential that admits 2n ? 1 functionally independent constants of the motion that are polynomial in the momenta, the maximum number possible. If these constants of the motion are all quadratic, then the system is second-order superintegrable, the most tractable case and the one we study here. Such systems have remarkable properties: multi-integrability and separability, a quadratic algebra of symmetries whose representation theory yields spectral information about the Schrödinger operator, and deep connections with expansion formulas relating classes of special functions. For n = 2 and for conformally flat spaces when n = 3, we have worked out the structure of the classical systems and shown that the quadratic algebra always closes at order 6. Here, we describe the quantum analogs of these results. We show that, for nondegenerate potentials, each classical system has a unique quantum extension.     

A Method for Estimation of the Parameters of the Primary Particle of an Extensive Air Shower by a High-Altitude Detector

A method for estimation of the parameters of the primary particle of an extensive air shower (EAS) by a high-altitude detector complex is described. This method was developed as part of the Pamir-XXI project. The results may be useful for other high-altitude projects and the EAS method in general. The specific configurations of optical detectors for Cherenkov EAS radiation and charged-particle detectors, the methods for data processing, and the attainable accuracy of reconstruction of parameters of primary particles (energy, direction, mass/type) are presented. The results primarily cover optical detectors that are suitable for studying EASs from primary nuclei in the range of energies E⁰ = 100 TeV–100 PeV and showers from primary γ-quanta with energies of E_γ ≥ 30 TeV. Grids of charged-particle detectors designed to determine the EAS direction and energy in the E⁰ = 1 PeV–1 EeV range are also considered. The obtained accuracy estimates are the upper limits of the actual experimental accuracies.     

Electrostatic self-force in the field of an (<Emphasis Type="Italic">n</Emphasis> + 1)-dimensional black hole: Dimensional regularization

The self-energy of a classical charged particle localized at a relatively large distance outside the event horizon of an (n + 1)-dimensional Schwarzschild–Tangherlini black hole for an arbitrary n ≥ 3 is calculated. An expression for the electrostatic Green function is derived in the first two orders of the perturbation theory. Dimensional regularization is proposed to be used to regularize the corresponding formally divergent expression for the self-energy. The derived expression for the renormalized self-energy is compared with the results of other authors.     

Untersuchungen zur Mehrfach-Emission von Sekundärelektronen

CuBe- and NaCl-targets are bombarded by single electrons (100–600 eV). The secondary electrons accelerated by 40 kV strike the crystal of a scintillation counter, backed by a multichannel analyser. The probabilityP _n of emission ofn=0, 1, 2, 3, ... secondaries can be found from the pulse height distribution. The probability distributionP _n =f(n) shows a characteristic deviation from aPoisson's distribution. There was no evidence that there is a preference for even numbers ofn as found byBarrington andAnderson.     

Field-theory methods in coagulation theory

Coagulating systems are systems of chaotically moving particles that collide and coalesce, producing daughter particles of mass equal to the sum of the masses involved in the respective collision event. The present article puts forth basic ideas underlying the application of methods of quantum-field theory to the theory of coagulating systems. Instead of the generally accepted treatment based on the use of a standard kinetic equation that describes the time evolution of concentrations of particles consisting of a preset number of identical objects (monomers in the following), one introduces the probability W(Q, t) to find the system in some state Q at an instant t for a specific rate of transitions between various states. Each state Q is characterized by a set of occupation numbers Q = {n ₁, n ₂, ..., n _g , ...}, where n _g is the total number of particles containing precisely g monomers. Thereupon, one introduces the generating functional Ψ for the probability W(Q, t). The time evolution of Ψ is described by an equation that is similar to the Schrödinger equation for a one-dimensional Bose field. This equation is solved exactly for transition rates proportional to the product of the masses of colliding particles. It is shown that, within a finite time interval, which is independent of the total mass of the entire system, a giant particle of mass about the mass of the entire system may appear in this system. The particle in question is unobservable in the thermodynamic limit, and this explains the well-known paradox of mass-concentration nonconservation in classical kinetic theory. The theory described in the present article is successfully applied in studying the time evolution of random graphs.     

Astrophysical <Emphasis Type="Italic">S</Emphasis>-factor of T(<Superscript>4</Superscript>He, γ)<Superscript>7</Superscript>Li reaction at <Emphasis Type="Italic">E</Emphasis><Subscript>cm</Subscript> = 15.7 keV

The astrophysical S-factor of the reaction T(⁴He, γ)⁷Li is measured for the first time at the center of mass energy E _cm = 15.7 keV, lower than the energy range of the Standard Big Bang Nucleosynthesis (SBBN) model. The experiment is performed on a Hall pulsed accelerator (TPU, Tomsk). An acceleration pulse length of 10 μs allows one to suppress the background of cosmic radiation and the ambient medium by five orders of magnitude. A beam intensity of ~ 5 × 10^{14 4}He⁺ ions per pulse allows one to measure an extremely low reaction yield. The yield of γ-quanta with the energies E _γ ⁰ = 2483.7 keV and E _γ ¹ = 2006.1 keV is registered by NaI(Tl) detectors with the efficiency ε = 0.331 ± 0.026. A method for direct measurement of the background from the chain of reactions T(⁴He, ⁴He)T→T(T, 2n)X→(n, γ) and/or (n, n′γ) which ends by neutron activation of materials surrounding the target is proposed and implemented in this study. The value of the astrophysical S-factor of the reaction T(⁴He, γ)⁷Li S _αt (E _cm = 15.7 keV) = 0.091 ± 0.032 keV b provides the choice from the set of experimental data for the astrophysical S _αt -factor in favor of experimental data [4] with S _αt (E _cm = 0) = 0.1067 ± 0.0064 keV b.     

Elementary-oscillator model for color centers with degenerate levels

Quantum transitions between nondegenerate and degenerate (with respect to angular momentum projection) levels of color centers in crystals are described in terms of classical electric-dipole oscillators. It is shown that, upon absorption of elliptically polarized exciting radiation, the system under study transfers to a definite state and the transition is described in general by an elliptical oscillator. An electric-dipole transition accompanied by the creation of a photon is described by a random vector, i.e., by an arbitrary elliptical oscillator lying in the corresponding plane. For an ensemble of n identically oriented centers undergoing a given transition, the luminescence intensity is described by a set of n/2 right-handed rotators and n/2 left-handed rotators. The results obtained are important for solving problems related to quantum information.     

Evolution of a Modified Binomial Random Graph by Agglomeration

In the classical Erd?s–Rényi random graph G(n, p) there are n vertices and each of the possible edges is independently present with probability p. The random graph G(n, p) is homogeneous in the sense that all vertices have the same characteristics. On the other hand, numerous real-world networks are inhomogeneous in this respect. Such an inhomogeneity of vertices may influence the connection probability between pairs of vertices. The purpose of this paper is to propose a new inhomogeneous random graph model which is obtained in a constructive way from the Erd?s-Rényi random graph G(n, p). Given a configuration of n vertices arranged in N subsets of vertices (we call each subset a super-vertex), we define a random graph with N super-vertices by letting two super-vertices be connected if and only if there is at least one edge between them in G(n, p). Our main result concerns the threshold for connectedness. We also analyze the phase transition for the emergence of the giant component and the degree distribution. Even though our model begins with G(n, p), it assumes the existence of some community structure encoded in the configuration. Furthermore, under certain conditions it exhibits a power law degree distribution. Both properties are important for real-world applications.