The effect of non-linear capacitances in the localization properties of aperiodic dual electric transmission lines

This study investigates the localization properties of dual electric transmission lines with non-linear capacitances. The V_C,n voltage across each capacitor is selected as a non-linear function of the electric charge q_n, i.e., V_C,n = q_n(1/C_n -ε_n|q_n|²)where C_n is the linear part of the capacitance and ε_n the amplitude of the non-linear term. We follow a binary distribution of values of ε_n, according to the Thue-Morse m-tupling sequence. The localization behavior of this non-linear case indicates that the case m = 2 does not belong to the m ≥ 3, family because when m changes from m = 2 to m = 3, the number of extended states diminishes dramatically. This proves the topological difference of the m = 2 and m = 3 families. However, by increasing m values, localization behavior of the m-tupling family resembles that of the m = 2, case because the system begins to regain its extended states. The exact same result was obtained recently in the study of linear direct transmission lines with m-tupling distribution of inductances. Consequently, we state that the localization behavior of the m-tupling family as a function of the m value is independent of both the linear and the non-linear system under study, but independent of the kind of transmission line (dual or direct). This is curious behavior of the m-tupling family and thus deserves more scholarly attention.     

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.     

Post-Newtonian parameter <Emphasis Type="Italic">γ</Emphasis> in generalized non-local gravity

We investigate the post-Newtonian parameter γ and derive its formalism in generalized non-local (GNL) gravity, which is the modified theory of general relativity (GR) obtained by adding a term m ^2n?2 R?^?n R to the Einstein-Hilbert action. Concretely, based on parametrizing the generalized non-local action in which gravity is described by a series of dynamical scalar fields ? ⁱ in addition to the metric tensor g _μν, the post-Newtonian limit is computed, and the effective gravitational constant as well as the post-Newtonian parameters are directly obtained from the generalized non-local gravity. Moreover, by discussing the values of the parametrized post-Newtonian parameters γ, we can compare our expressions and results with those in Hohmann and Järv et al. (2016), as well as current observational constraints on the values of γ in Will (2006). Hence, we draw restrictions on the nonminimal coupling terms F? around their background values.     

Monogamy Relations in Terms of Tsallis-Q Entropy in any Dimensional System

Monogamy of entanglement is a fundamental property of multipartite entangled states. In this article, due to the convexity of Trρ^q with respect to q when q ≥ 1, we give a monogamy-like relation in terms of Tsallis-q entanglement entropy of assistance (TqEEA) for pure states over an n- partite any dimensional system and monogamy-like relations in terms of Tsallis-q entanglement entropy (TqEE) for mixed states for any dimensional system, we also give a lower bound for the TqEE of a four-partite pure state. At last, we show that the generalized W-class states satisfy the polygamy relation in terms of TqEE when q = 2.     

Influence of the dimension of a polycrystalline film and the optical anisotropy of crystallites on the effective dielectric constant of the film

The dimension D of a polycrystalline film and the optical anisotropy m = ε_z/ε_x of uniaxial crystallites with the principal components ε_x = ε_y and ε_z of the tensor of the dielectric constant have been shown to produce a strong influence on the effective dielectric constant ε_D^* and the effective refractive index n_D^* = (ε_D^*)^1/2 of the film in the optical transparency region, as well as on the boundaries of the intervals B_Dl ≤ ε_D^* ≤ B_Du. The intervals Δ₂(m) = B_2l–B_2u and Δ₃(m) = B_3l–B_3u are separated by a gap for m in the range 1 < m < 2, whereas the theoretical dependence ε₂^*(m) is separated by a gap from the interval Δ₃(m) for m in the range 1 < m < 4. This is confirmed by a comparison of the experimental (n_oP) and theoretical (n_D^*) ordinary refractive indices for uniaxial polycrystalline films of the conjugated polymer poly(p-phenylene vinylene) (PPV) with uniaxial crystallites and appropriate values of m. In the visible transparency region of the PPV films with a change in m(λ) in the range 2 < m(λ) < 3 due to the dependence of the components ε_x,z(λ) on the light wavelength λ, the refractive indices n_oP²(λ) = ε_oP(λ) are consistent with the theoretical values of ε₂^*(λ) and lie outside the interval Δ₃(m). For m(λ) > 3 near the electronic absorption band of the crystallites, the values of ε_oP(λ) lie in the region of the overlap of the intervals Δ₂(m) and Δ₃(m). The boundaries mc of the range 1 < m < m_c are determined, for which the interval Δ₂(m) is separated by a gap from the dependences ε₃^*(m) corresponding to the effective medium theory with spherical crystallites and hierarchical models of a polycrystal, as well as from the proposed new dependence ε₃^*(m).     

Die Abweichungen von den Cauchy-Relationen

Qualitative rules for the deviations from the Cauchy relations are derived from experimental data. These departures are the components of a second rank tensor. The coefficients of “lateral interaction”c _iijj dominate in most cases over the correspondent shear resistancesc _ijij. Extreme effects of this type are generated by asymmetric lattice particles. Covalent bonds and other strong bonds with preferential orientation as well as strong overlap cause opposite effects. The departures from the Cauchy relations and the atomistic binding properties are very closely correlated.     

Electron–positron pair production from vacuum in the field of high-intensity laser radiation

The works dealing with the theory of e⁺e^– pair production from vacuum under the action of highintensity laser radiation are reviewed. The following problems are discussed: pair production in a constant electric field E and time-variable homogeneous field E(t); the dependence of the number of produced pairs \({N_{{e^ + }{e^ - }}}\) on the shape of a laser pulse (dynamic Schwinger effect); and a realistic three-dimensional model of a focused laser pulse, which is based on exact solution of Maxwell’s equations and contains parameters such as focal spot radius R, diffraction length L, focusing parameter Δ, pulse duration τ, and pulse shape. This model is used to calculate \({N_{{e^ + }{e^ - }}}\) for both a single laser pulse (n = 1) and several (n ≥ 2) coherent pulses with a fixed total energy that simultaneously “collide” in a laser focus. It is shown that, at n ? 1, the number of pairs increases by several orders of magnitude as compared to the case of a single pulse. The screening of a laser field by the vapors that are generated in vacuum, its “depletion,” and the limiting fields to be achieved in laser experiments are considered. The relation between pair production, the problem of a quantum frequency-variable oscillator, and the theory of groups SU(1, 1) and SU(2) is discussed. The relativistic version of the imaginary time method is used in calculations. In terms of this version, a relativistic theory of tunneling is developed and the Keldysh theory is generalized to the case of ionization of relativistic bound systems, namely, atoms and ions. The ionization rate of a hydrogen-like ion with a charge 1 ≤ Z ≤ 92 is calculated as a function of laser radiation intensity (F and ellipticity ρ.     

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 Local Structure of Zero Mode¶Producing Magnetic Potentials

We consider the class of continuous magnetic potentials on ?³ which decay as o(|x|^{? 1}). Within this class it is shown that the set of potentials whose associated Weyl-Dirac operator produces zero modes with multiplicity m forms a smooth submanifold of co-dimension m ² when m= 0, 1, 2, and is contained in a smooth submanifold of co-dimension 2m? 1 when m≥ 3.     

Higher derivative extensions of 3<Emphasis Type="Italic">d</Emphasis> Chern–Simons models: conservation laws and stability

We consider the class of higher derivative 3d vector field models with the field equation operator being a polynomial of the Chern–Simons operator. For the nth-order theory of this type, we provide a general recipe for constructing n-parameter family of conserved second rank tensors. The family includes the canonical energy-momentum tensor, which is unbounded, while there are bounded conserved tensors that provide classical stability of the system for certain combinations of the parameters in the Lagrangian. We also demonstrate the examples of consistent interactions which are compatible with the requirement of stability.     

Quark-antiquark composite systems: The Bethe-Salpeter equation in the spectral-integration technique in the case of different quark masses

The Bethe-Salpeter equations for quark-antiquark composite systems with different quark masses, such as \(q\bar s(with q = u,d),q\bar Q\), and \(s\bar Q\) (with Q = c, b), are written in terms of spectral integrals. For mesons characterized by the mass M, spin J, and radial quantum number n, the equations are written for the (n, M²) trajectories with fixed J. The mixing between states with different quark spin S and angular momentum L is also discussed.     

Lagrangian structure functions in hydrodynamic turbulence

Based on a solution of the Navier-Stokes equations for the inertial range of fully developed turbulence, a statistical theory is developed to determine the Lagrangian structure functions K _n (τ). Over times τ shorter than the large-scale correlation time τ_c, they obey scaling relations of the form K _n (τ) ∞ \(\tau ^{\zeta _n } \). Analytical expressions are derived for ζ _n . A detailed comparison between the theory and the experimental results presented in [1] demonstrates complete quantitative agreement. A new concept is introduced in turbulence theory: the correlation R _n (τ) between tracer-particle positions on a Lagrangian trajectory. It is shown that the position correlation functions R _n exhibit universal scaling behavior for n > 3.     

Some exact results for the three-layer zamolodchikov model

In this talk, we present our recent results on the three-layer Zamolodchikov model. We discuss solutions to the Bethe ansatz equations following from functional relations. We consider two regimes I and II that differ by the signs of the spherical sides (a₁, a₂, a₃) → (?a₁, ?a₂, ?a₃). Also, we accept the two-line hypothesis for regime I and the one-line hypothesis for regime II. In the thermodynamic limit, we derive integral equations for distribution densities and solve them exactly. Using this solution, we calculate the partition function for the three-layer Zamolodchikov model and check the compatibility of this result with functional relations. We also discuss the reasons for the discrepancy with Baxter’s result of 1986.     

A spectroscopic prism coupler for measuring the refractive indices and thicknesses of dielectric films

A spectroscopic prism coupler is created for measuring refractive indices n_f and thicknesses H_f of dielectric films. The operating principle of the device is based on the simultaneous resonance excitation of several waveguide modes in a film by a focused TE or TM polarized light beam in the geometry of frustrated total internal reflection. Calculations of n_f and H_f are performed using measured angular positions θ_m of dark m-lines in the cross section of the specularly reflected beam. Using obtained angles θ_m, we can calculate effective refractive indices β_m of modes. By solving a set of nonlinear dispersion equations for the modes of a planar waveguide, we can calculate refractive index n_f and thickness H_f of a film. The proposed prism coupler has no moving parts and allows us to measure the optical parameters of films 0.5–10 μm thick in the 400–1100 nm range of wavelengths. The device can also be used as a spectroscopic refractometer for measuring the refractive indices of bulk media. The device is used to measure refractive index and thickness of a SiO film and the refractive index of TF4 glass.     

Low energy frontier: Physics with polarized cold neutrons

Recent developments in investigations of beta decay of the free neutron are discussed. Measurements of the neutron lifetime τ _n and the electron emission asymmetry A _n are a classic source of determination of the Standard Model parameters G _v , G _A and λ _n . Combined with the results of the muon decay experiments, the nuclear superallowed 0→0 transitions and decays of particles containing heavy quarks, they provide tests of the SM assumptions: the unitarity of the CKM matrix, the number of the neutrino families, or the CVC hypothesis. In contrast, more complex correlations between the spins and the momenta of the emitted particles, (e.g. B _n , D _n , R _n or G _n ), are uniquely sensitive to the so called “Physics beyond the Standard Model”. Thus the question of the right handed bosons, the admixture of the scalar or tensor interaction, with or without time reversal violating terms, may be addressed separately in a dedicated, single experiment. Further development of powerful beams of polarized cold neutrons and sources of ultracold neutrons is imperative for progress in these studies.     

Reconstruction of constant slow-roll inflation

Using the relations between the slow-roll parameters and the power spectra for the single field slow-roll inflation, we derive the scalar spectral tilt n_s and the tensor to scalar ratio r for the constant slow-roll inflation, and obtain the constraint on the slow-roll parameter η from the Planck 2015 results. The inflationary potential for the constant slow-roll inflation is then reconstructed in the framework of both general relativity and the scalar-tensor theory of gravity, and compared with the recently reconstructed E model potential. In the strong coupling limit, we show that the η attractor is reached.     

Palatini formulation of <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>, <Emphasis Type="Italic">T</Emphasis>) gravity theory,and its cosmological implications

We consider the Palatini formulation of f(R, T) gravity theory, in which a non-minimal coupling between the Ricci scalar and the trace of the energy-momentum tensor is introduced, by considering the metric and the affine connection as independent field variables. The field equations and the equations of motion for massive test particles are derived, and we show that the independent connection can be expressed as the Levi-Civita connection of an auxiliary, energy-momentum trace dependent metric, related to the physical metric by a conformal transformation. Similar to the metric case, the field equations impose the non-conservation of the energy-momentum tensor. We obtain the explicit form of the equations of motion for massive test particles in the case of a perfect fluid, and the expression of the extra force, which is identical to the one obtained in the metric case. The thermodynamic interpretation of the theory is also briefly discussed. We investigate in detail the cosmological implications of the theory, and we obtain the generalized Friedmann equations of the f(R, T) gravity in the Palatini formulation. Cosmological models with Lagrangians of the type \(f=R-\alpha ^2/R+g(T)\) and \(f=R+\alpha ^2R^2+g(T)\) are investigated. These models lead to evolution equations whose solutions describe accelerating Universes at late times.     

Kramers–Kronig Relations in Representation of Modulation Polarimetry by an Example of the Transmission Spectra of GaAs Crystal

The increments of the real and imaginary components of the complex refractive index ΔN = Δn–iΔk of a lightly doped GaAs crystal with a donor concentration of ~10¹⁶ cm^–3 have been measured using modulation polarimetry. It is shown that, within this representation, the birefringence and dichroism spectra (Δn(ω) and Δk(ω), respectively) obtained in the transparency window of a sample subjected to probe strain are derivatives of the corresponding functions: Δn(ω) ≈ dn/dω and Δk(ω) ≈ dk/dω. The experimental characteristics and primary dependences n(ω) and k(ω) derived from them by graphical integration are in agreement with the results of other researchers and measurements carried out by independent methods. The results obtained are compared (taking into account the integral (Kramers–Kronig) relations) with the resonance parameters: amplitude and phase in the Drude–Lorenz model. Agreement between the experimental characteristics and theoretical model predictions can be obtained by choosing an appropriate value of resonance damping parameter.     

Warm Gauge-Flation with General Dissipative Coefficient

In this work, we study the effects of generalized dissipative coefficient on the slow-roll inflation driven by non-Abelian gauge field minimally coupled to gravity. The dynamics of warm intermediate and logamediate inflationary models during weak and strong dissipative regimes is analyzed. In both cases, we explore effective scalar potential, slow-roll parameters, scalar and tensor power spectra, scalar spectral index and tensor to scalar ratio under slow-roll conditions. We conclude that our gauge-flationary model with generalized dissipative coefficient remains consistent with the recent data for dissipative parameter m = 3 and m = 1 for weak and strong dissipative eras, respectively.     

Quark-antiquark composite systems: The Bethe-Salpeter equation in the spectral-integration technique

The Bethe-Salpeter equations for the quark-antiquark composite systems, q\(\bar q\), are written in terms of spectral integrals. For the q\(\bar q\) mesons characterized by the mass M, spin J, and radial quantum number n, the equations are presented for the following (n, M²) trajectories: π _J , η _J , a _J , f _J , ρ _J , ω _J , h _J , and b _J .