The signal photon flux,background photons and shot noise in electromagnetic response of high-frequency relic gravitational waves

On the basis of the electromagnetic response of high frequency relic gravitational waves (HFRGWs), we research on more accurate calculation of signal (i.e. transverse perturbative photon flux (PPF)) and background photons flux (BPF) in the sycro-resonance electromagnetic system, which consists of Gaussian beam (GB), a static magnetic field and fractal membranes. According to the relationship between frequency of gravitational waves and its dimensionless amplitude, we focus on the HFRGWs with ν _g  = 2.9 GHz, h ~ 10^?30 in the pre-big bang and quintessential inflationary models. The results show the peak value of the transverse BPF (~ 10²⁰ s^?1) is around |x| = 0.08 m, where |x| is the transverse distance to the longitudinal symmetrical surface of the GB, while the maximum transverse PPF always appears at x = 0 (\({N^{(1)}_{x} \sim 2.60\times10^{2}\,{\rm s}^{-1}}\) with the optimal phase difference between the GB and the resonant component of the HFRGWs δ = (n + 0.9)π, n = 0, 1, 2 . . .). However, the observable PPF should be ~ 1.19 × 10² s^?1 because of the stochastic nature of the HFRGWs’ phase. Since the decay speed of BPF is much quicker than PPF, it is hopeful to figure out the signal in some optimal regions. Moreover, we compare the decay speed of BPF and PPF in nature mode, and find the threshold value of x where PPF exceeds to BPF. It demonstrates that the limitation of our detection sensitivity comes from the strength of PPF rather than swamping by BPF. On the other hand, with the fractal membrane, the comparison between BPF and PPF provides the optimal detection area \({x\in[0.28,1]}\) m. In addition, through the calculation of shot noise and conservative estimation, we find that our sensitivity is h = 10^?26 in 4 months signal accumulate time.     

On the Generation and Detection of High-Frequency Gravitational Waves Optically Excited in Dielectric Media

The possibility of generating and detecting high-frequency gravitational waves based on nonlinear-optical processes in dielectric media at their excitation by intense laser radiation of visible or ultraviolet ranges is analyzed. The theory predicts the feasibility of the Hertz gravitational laboratory experiment in which the parametric conversion of intense laser radiation with frequency ω₀ = 2πf₀ (f₀ = 10¹⁴ ? 10¹⁵ Hz) to a gravitational wave with frequency ω _g = 2ω₀ and the reverse process of gravitational radiation reconversion to optical radiation are implemented in the condensed dielectric medium.     

Experimentelle Untersuchung von Elektronen-Photonen-Kaskaden in Blei-Szintillator-Anordnungen für Primärenergien zwischen 100 und 440 MeV

Showers generated by electrons of 200 and 440 MeV energy in single lead plates of 2, 5, and 10 radiation lengths are measured in scintillator material (NE 102 A) varying between 1.24 and 10.5 g/cm². The mean energy deposited in a scintillator is derived fromNagel's Monte-Carlo calculations. The photon contributionn _γ to the total pulseheight is of the order 15% near shower maximum t_max, it dominates the electron contributionn _e in a 3 cm thick scintillator for shower depthst ≧ 4.2 · t_max. The slope of the total ionizationn _e+n _γ behind the shower maximum can be approximated byn(t) ～ exp(?0.264t). The shower absorption in scintillator depends on the thicknessx (g/cm²) as exp (?0.068x). An arrangement of counter trays, scintillators and lead plates is calibrated with electrons between 100 and 440 MeV energy. A suitably defined track-lengthS is shown to give minimum error in energy measurement and to depend linearly on electron energy. The track-length constant of 22 MeV/r.l. is compared with the results of other authors.     

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.     

Inflation of the early cold Universe filled with a nonlinear scalar field and a nonideal relativistic Fermi gas

We consider a possible scenario for the evolution of the early cold Universe born from a fairly large quantum fluctuation in a vacuum with a size a ₀ ? l _P (where l _P is the Planck length) and filled with both a nonlinear scalar field φ, whose potential energy density U(φ) determines the vacuum energy density λ, and a nonideal Fermi gas with short-range repulsion between particles, whose equation of state is characterized by the ratio of pressure P(n _F ) to energy density ε(n _F ) dependent on the number density of fermions n _F . As the early Universe expands, the dimensionless quantity ν(n _F ) = P(n _F )/ε(n _F ) decreases with decreasing n _F from its maximum value ν_max = 1 for n _F → ∞ to zero for n _F → 0. The interaction of the scalar and gravitational fields, which is characterized by a dimensionless constant ξ, is proportional to the scalar curvature of four-dimensional space R = κ[3P(n _F )–ε(n _F )–4λ] (where κ is Einstein’s gravitational constant), and contains terms both quadratic and linear in φ. As a result, the expanding early Universe reaches the point of first-order phase transition in a finite time interval at critical values of the scalar curvature R = R _c =–μ²/ξ and radius a _c ? a ₀. Thereafter, the early closed Universe “rolls down” from the flat inflection point of the potential U(φ) to the zero potential minimum in a finite time. The release of the total potential energy of the scalar field in the entire volume of the expanding Universe as it “rolls down” must be accompanied by the production of a large number of massive particles and antiparticles of various kinds, whose annihilation plays the role of the Big Bang. We also discuss the fundamental nature of Newton’ gravitational constant G _N .     

Experimental investigation of ρ<Superscript>0</Superscript> photoproduction on the pion in the H1 experiment

Experimental results on quasielastic photoproduction of the ρ⁰ meson in association with a neutron, obtained at the HERA collider, are presented. The total and differential cross sections of the γp → ρ⁰ nπ⁺ reaction at the positron–proton center-of-mass energy of √s =319 GeV are measured. The data collected with the H1 detector in 2006 and 2007 correspond to an integrated luminosity of 1.16 pb^?1. The kinematic region of the photon–proton cms energy of 20 < W _γp <100 GeV, photon virtuality of Q ² < 2 GeV², and the ρ⁰ transverse momentum below 1 GeV/c is analyzed. Secondary neutrons with energies x _L > 0.35 (in proton-energy units) and emission angles below 0.75 mrad are selected. The model of double peripheral exchange, in which the ρ⁰ is elastically produced via the photon interaction with the virtual pion from the proton–neutron vertex, is employed for interpreting the results. The cross section for the ρ⁰ elastic photoproduction on the pion, γπ⁺→ ρ⁰π⁺, is extracted in the one-pion-exchange approximation. The magnitude of the cross section suggests that the γp → ρ⁰ nπ⁺ reaction is significantly affected by absorption.     

Differential-geometric structures associated with Lagrangians corresponding to scalar physical fields

The paper is devoted to the investigation, using the method of Cartan–Laptev, of the differential-geometric structure associated with a Lagrangian L, depending on a function z of the variables t, x ¹,...,x ⁿ and its partial derivatives. Lagrangians of this kind are considered in theoretical physics (in field theory). Here t is interpreted as time, and x ¹,...,x ⁿ as spatial variables. The state of the field is characterized by a function z(t, x ¹,..., x ⁿ ) (a field function) satisfying the Euler equation, which corresponds to the variational problem for the action integral. In the present paper, the variables z(t, x ¹,..., x ⁿ are regarded as adapted local coordinates of a bundle of general type M with n-dimensional fibers and 1-dimensional base (here the variable t is simultaneously a local coordinate on the base). If we agree to call t time, and a typical fiber an n-dimensional space, then M can be called the spatiotemporal bundle manifold. We consider the variables t, x ¹,...,x ⁿ , z (i.e., the variables t, x ¹,...,x ⁿ with the added variable z) as adapted local coordinates in the bundle H over the fibered base M. The Lagrangian L, which is a coefficient in the differential form of the variational action integral in the integrand, is a relative invariant given on the manifold J ¹ _H (the manifold of 1-jets of the bundle H). In the present paper, we construct a tensor with components Λ⁰⁰, Λ⁰ⁱ , Λ ^ij (Λ ^ij = Λ ^ji ) which is generated by the fundamental object of the structure associated with the Lagrangian. This tensor is an invariant (with respect to admissible transformations the variables t, x ¹,...,x ⁿ , z) analog of the energy-momentum tensor of the classical theory of physical fields. We construct an invariant I, a vector G ⁱ , and a bivalent tensor G ^jk generated by the Lagrangian. We also construct a relative invariant of E (in the paper, we call it the Euler relative invariant) such that the equation E = 0 is an invariant form of the Euler equation for the variational action integral. For this reason, a nonvariational interpretation of the Euler equation becomes possible. Moreover, we construct a connection in the principal bundle with base J ² H (the variety of 2-jets of the bundle H) and with the structure group GL(n) generated by the structure associated with the Lagrangian.     

The electron energy spectrum and superconducting transition temperature of strongly correlated fermions with three-center interactions

The renormalizations of the fermionic spectrum are considered within the framework of the t-J* model taking into account three-center interactions (H₍₃₎) and magnetic fluctuations. Self-consistent spin dynamics equations for strongly correlated fermions with three-center interactions were obtained to calculate quasi-spin correlators. A numerical self-consistent solution to a system of ten equations was obtained to show that, in the nearest-neighbor approximation, simultaneously including H₍₃₎ and magnetic fluctuations at n>n₁ (n₁ ≈ 0.72 for 2t/U = 0.25) caused qualitative changes in the structure of the energy spectrum. A new Van Hove singularity is then induced in the density of states, and an additional maximum appears in the T_c(n) concentration dependence of the temperature of the transition to the superconducting phase with order parameter symmetry of the d _x ²?y² type.     

Coulomb Rydberg electron <Emphasis Type="Italic">L</Emphasis>-mixing in collisions with atomic ions

The cross sections of the Rydberg electron L-mixing in a hydrogen atom and a hydrogen-like ion are calculated for slow collisions with atomic ions H*(n, L) + A⁺ = H*(n, L′) + A⁺ without variation of the principal quantum number n. The probability of the L-mixing L → L′ is associated with the quantum interference of the wave functions of adiabatic states, i.e., with the mixing of the time phases of these functions exp(?i∫E _k (t)dt). The effective cross section of such L-mixing for the states with n = 28 are 4–5 orders of magnitude greater than the cross sections determined in previous investigations. The expansion coefficients of spherical Coulomb wave functions in terms of parabolic ones and vice versa, which are necessary for determining cross sections, are calculated on the basis of a comprehensive analysis of the spatial properties of these functions.     

Lattice instability induced by 3<Emphasis Type="Italic">d</Emphasis> impurities in II–VI compound semiconductors

Nickel-impurity-induced transverse displacements of ions in a Zn_1?xNi_xSe lattice (x = 0.0025) were detected. This type of displacement correlates with macroscopic distortions of a crystal associated with transverse ultrasonic waves that are propagated along the 〈110〉 direction. The shear instability is assumed to be due to the hybridization of the sp³ bonds with the 3d states of the impurity centers.     

Reliability of the data on the cross sections of the partial photoneutron reaction for <Superscript>63,65</Superscript>Cu and <Superscript>80</Superscript>Se nuclei

The cross sections of partial photoneutron reactions are evaluated for the ^63,65Cu and ⁸⁰Se isotopes. The cross sections are free of systematic uncertainties from shortcomings of the experimental methods for neutron multiplicity sorting based on measurements of neutron energy used in experiments with quasimonoenergetic annihilation photon beams. An experimental-theoretical method is used to evaluate cross sections σ^eval(γ, in)= F_i^theor σ^exp(γ, xn), where ratios F_i^theor = σ^theor(γ, in)/σ^theor(γ, xn) = σ^theor(γ, in)/σ^theor[(γ, 1n) + 2(γ, 2n) + …] are calculated using a combined model of photonuclear reactions, and σ^exp(γ, xn) is the experimental cross section of the neutron yield reaction free from neutron multiplicity sorting problems. The cross sections are evaluated for reactions (γ, 1n) and (γ, 2n) for the ^63,65Cu and ⁸⁰Se isotopes, and for the total photoneutron reaction σ(γ, Sn) = σ[(γ, 1n) + (γ, 2n) + …]. It is shown that noticeable deviations of the experimental cross sections from the evaluated values result from the unreliable sorting of neutrons between the channels with multiplicities 1 and 2.     

The reactions N14(n, α)B11 and N14(n,t)C12 observed with a gridded ionization chamber

The cross sections for the reactions N¹⁴(n, α)B¹¹ and N¹⁴(n, t)C¹² have been measured in the neutron energy range 4.0 to 6.4 MeV and at 2.5 MeV. Mono-energetic neutrons were produced in the D(d, n) He³ reaction using a gas target. The (n, α) and (n, t) disintegrations were detected in a gridded ionization chamber filled with an argonnitrogen mixture. The response of the chamber under different operation conditions is described. The excitation functions, measured with a neutron energy resolution of 40 to 50 keV, are given for theα ₀ group from the N¹⁴(n,α)B¹¹ reaction over the entire neutron energy range and for theα ₁ group and the t₀ group from N¹⁴(n, t) C¹² for neutron energies above 4.3 and 5.6 MeV, respectively.     

Nuclear magnetic relaxation induced by the relaxation of electron spins

A physical mechanism responsible for the relaxation of nuclear spins coupled by the hyperfine interaction to relaxed electron spins in materials with spin ordering is proposed. The rate of such induced nuclear spin relaxation is proportional to the dynamic shift of the nuclear magnetic resonance (NMR) frequency. Therefore, its maximum effect on the NMR signal should be expected in the case of nuclear spin waves existing in the system. Our estimates demonstrate that the induced relaxation can be much more efficient than that occurring due to the Bloch mechanism. Moreover, there is a qualitative difference between the induced and Bloch relaxations. The dynamics of nuclear spin sublattices under conditions of the induced relaxation is reduced to the rotation of m₁ and m₂ vectors without any changes in their lengths (m ₁ ² (t) = m ₂ ² (t) = m ₀ ² (t)= const). This means that the excitation of NMR signals by the resonant magnetic field does not change the temperature T _n of the nuclear spin system. This is a manifestation of the qualitative difference between the induced and Bloch relaxations. Indeed, for the latter, the increase in T _n accompanying the saturation of NMR signals is the dominant effect.     

Congratulations to Akusticheskii Zhurnal on the occasion of its 50th anniversary. Vibrations of spherical inclusions in elastic solids

Variational principles are derived for the analysis of dynamical phenomena associated with spherical inclusions embedded in homogeneous isotropic elastic solids. The starting point is Hamilton’s principle, with the material properties assumed to vary only with the radial distance r from the origin. Attention is restricted to disturbances that are symmetric about the polar (z) axis, such that the nonzero displacement components in spherical coordinates, u _r and u_θ, are independent of the polar coordinate φ. The symmetry allows for a decoupling of the polar components, the nth of which is described by U _{r, n} (r, t)P _n (cosθ) and U_{θ, n}(r, t)dP _n /dθ. A variational principle is subsequently derived for the field quantities U _{r, n} and U_{θ, n}. Concepts analogous to those of the theory of matched asymptotic expansions are used to embellish the principle in order to allow for the damping associated with the outward radiation of elastic waves. Examples illustrating the use of the variational principle for formulating plausible lumped-parameter models are given for the cases of n = 0 and n = 1.     

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.     

Kinetic freeze-out s pectra of identified particles produced in p–Pb collisions at $$\sqrt {s_{NN} }$$ = 5.02 TeV

We study the transverse momentum spectra of identified pions (π^– + π⁺), kaons ((K ^– + K ⁺), K ₀ ^s ), protons (p + p?) and lambda hyperons (Λ + Λ?) produced at mid-rapidity (0 < y _cm < 0.5) in most central (0?5)% p–Pb collisions at \(\sqrt {s_{NN} }\) = 5.02 TeV in comparison with a Unified Statistical Thermal Freeze-out Model (USTFM). The measurements for pions are reported upto p _T = 3 GeV, the kaons (K ^– + K ⁺) are reported upto p _T = 2.5 GeV, K ₀ ^s is reported upto p _T = 7 GeV, and the baryons (protons and lambda hyperons) are reported upto p _T = 3.5 GeV. A good agreement is seen between the calculated results and the experimental data points taken from the ALICE experiment. The transverse momentum spectra are found to be flatter for heavy particles than for light particles. Bulk freeze-out properties in terms of kinetic freeze-out temperature and the transverse collective flow velocity are extracted from the fits of the transverse momentum spectra of these hadrons. The effect of resonance decay contributions has also been taken care of.     

The electrical conductance growth of a metallic granular packing

We report on measurements of the electrical conductivity on a two-dimensional packing of metallic disks when a stable current of ~1 mA flows through the system. At low applied currents, the conductance σ is found to increase by a pattern σ(t) = σ _∞ ? Δσ E _α [ ? (t/τ) ^α ], where E _α denotes the Mittag-Leffler function of order α ∈ (0,1). By changing the inclination angle θ of the granular bed from horizontal, we have studied the impact of the effective gravitational acceleration g _eff = gsinθ on the relaxation features of the conductance σ(t). The characteristic timescale τ is found to grow when effective gravity g _eff decreases. By changing both the distance between the electrodes and the number of grains in the packing, we have shown that the long term resistance decay observed in the experiment is related to local micro-contacts rearrangements at each disk. By focusing on the electro-mechanical processes that allow both creation and breakdown of micro-contacts between two disks, we present an approach to granular conduction based on subordination of stochastic processes. In order to imitate, in a very simplified way, the conduction dynamics of granular material at low currents, we impose that the micro-contacts at the interface switch stochastically between two possible states, “on” and “off”, characterizing the conductivity of the micro-contact. We assume that the time intervals between the consecutive changes of state are governed by a certain waiting-time distribution. It is demonstrated how the microscopic random dynamics regarding the micro-contacts leads to the macroscopic observation of slow conductance growth, described by an exact fractional kinetic equations.     

Self-gravitating Brownian particles in two dimensions: the case of N = 2 particles

We study the motion of N = 2 overdamped Brownianparticles in gravitational interaction in a space of dimensiond = 2. This is equivalent to the simplified motion of twobiological entities interacting via chemotaxis when time delay anddegradation of the chemical are ignored. This problem also bearssimilarities with the stochastic motion of two point vorticesin viscous hydrodynamics [O. Agullo, A. Verga, Phys. Rev. E 63,056304 (2001)]. We analytically obtain the probability density offinding the particles at a distance r from each other at timet. We also determine the probability that the particles havecoalesced and formed a Dirac peak at time t(i.e. the probability that the reduced particle has reached r = 0at time t). Finally, we investigate the meansquare separation \(\langle\) r ² \(\rangle\) and discuss the proper formof the virial theorem for this system. The reduced particle has anormal diffusion behavior for small times with a gravity-modifieddiffusion coefficient \(\langle\) r ² \(\rangle\) = r ₀ ² + (4k _B /ξ μ)(T–\(T_{*}\))t, wherek _B \(T_{*}\) = Gm ₁ m ₂/2 is a critical temperature, and an anomalousdiffusion for large times \(\langle\) r ² \(\rangle\) \(\propto\) \(t^{1-T_*/T}\). As a by-product, our solution also describes thegrowth of the Dirac peak (condensate) that forms at large time inthe post collapse regime of the Smoluchowski-Poisson system (orKeller-Segel model in biology) for T < T _c = GMm/(4k _B ). We find thatthe saturation of the mass of the condensate to the total mass isalgebraic in an infinite domain and exponential in a boundeddomain. Finally, we provide the general form of the virial theoremfor Brownian particles with power law interactions.