Scattering the Geometry of Weighted Graphs

Given two weighted graphs (X, b_k, m_k), k =?1,2 with b₁ ～ b₂ and m₁ ～ m₂, we prove a weighted L¹-criterion for the existence and completeness of the wave operators W_±(H₂, H₁, I_1,2), where H_k denotes the natural Laplacian in ?²(X, m_k) w.r.t. (X, b_k, m_k) and I_1,2 the trivial identification of ?²(X, m₁) with ?²(X, m₂). In particular, this entails a general criterion for the absolutely continuous spectra of H₁ and H₂ to be equal.     

Quantifying Correlations via the Wigner-Yanase-Dyson Skew Information

In this paper, based on a discussion about the Wigner-Yanase-Dyson (WYD) skew information, the measure F_a,α(ρ_ab) for correlations in terms of the WYD skew information is introduced and discussed. The following conclusions are obtained. For a classical-quantum state ρ_ab, F_a,α(ρ_ab)=0 if and only if ρ_ab is a product state; F_a,α(ρ_ab) is locally unitary invariant and convex on the set of states with the fixed marginal ρ_a; F_a,α(ρ_ab) decreases under local random unitary operation on H_b; For a quantum-classical state ρ_ab, F_a,α(ρ_ab) decreases under local operation on H_b; Lastly, F_a,α(ρ_ab) is computed for the pure states and the Bell-diagonal states, 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 .     

Influence of the probe sizes on the parameters of the surface morphology of hemispherical-grain polysilicon films: Estimation via atomic-force microscopy

The influence of probe sizes on the basic surface-morphology parameters of hemispherical-grain polysilicon films which possess substantial surface roughness and non-Gaussian height distribution functions with appreciable negative skewness is studied. The dependences between the basic surface morphology parameters S _dr , S _q , S _al , S _z , S _v , S _p , and S _sk defined by the ISO 25178-2:2012 standard and the probe width-to-tip height (W/L) ratio are determined. It is ascertained that the relative increase S _dr in the surface area is most sensitive to the “degree of sharpness” (W/L ratio) and, on the contrary, the autocorrelation length S _al is least sensitive. Hemispherical-grain silicon films with considerable parameter S _dr can be employed as test samples in estimating the degree of sharpness of a probe.     

The structure of a vortex line and the lower critical field in superconducting alloys

The structure of an isolated vortex line, and the lower critical fieldH _c 1, is calculated by means of the generalized Ginzburg-Landau (GL) theory for arbitrary values of the GL-parameterk(≧1/√2) and the mean free pathl at temperaturesT in the vicinity ofT _c . The free energy functional including the corrections of order [1?(T/T _c )] to the GL-functional is derived exactly. The corresponding Euler-Lagrange equations determining the zero-order (GL) contributions and the corrections of order [1?(T/T _c )] to the order parameter,f(r), and the superfluid velocity,v(r), have been solved numerically. The shapes of the first-order corrections off(r), v(r), and the magnetic field,h(r) are found to depend markedly, for a given value ofκ, on a second parameter,α=0.882(ξ ₀ /l) (whereξ ₀ is theBCS-coherence-distance). The deviations from the GL-solutions become largest forh(r) at parameter valuesk≈ 1 andα ≈ 0(the deviation ofh(0) is about 6% atT=0.9T _c forκ=1 andα=0). The ratioH _c1/H _c (where the thermodynamic criticalH _c has the BCS-temperature-dependence) is found to increase slightly in the “clean” limit (α=0), and to decrease slightly in the “dirty” limit (α=∞) asT decreases (the variation ofH _c 1/H _c is always less than 3% for arbitrary values ofκ andα asT decreases fromT _c to 0.9T _c ).     

Change in the lattice properties and melting temperature of a face-centered cubic iron under compression

All four parameters of the Mie–Lennard-Jones pair interatomic potential have been determined, and the state equation (P) and baric dependences of the lattice properties of an fcc iron are calculated using a previously proposed method. The dependences have been studied for the following properties: Debye temperature; the first, second, and third Gruneisen parameters; isothermal bulk modulus B _T and B′(P); isochoric specific heat C _v and C _v ′(P); isobaric specific heat C _p ; coefficient of thermal expansion α _p and α _p ′(P); specific surface energy σ and σ′(P). Calculations performed along two isotherms (1500 and 3000 K) have shown good agreement with the experimental data. Analytical approximations of the baric dependences for B′(P), α _p (P), C _p (P), and σ′(P) have been obtained, and it is shown that at P → ∞ the functions B _T (P) and σ(P) change linearly, while the functions α _p′(P) and C _p ′(P) tend to zero. The calculated baric dependence of the melting temperature shows good agreement with the experimental data.     

On the energy transport velocity in a dissipative medium

An exact definition of the group velocity v _g is proposed for a wave process with arbitrary dispersion relation ω = ω′(k) + iω″(k). For the monochromatic approximation, a limit expression v _g (k) is obtained. A condition under which v _g (k) takes the form of the Kuzelev–Rukhadze expression [1] dω′(k)/dk is found. In the general case, it appears that v _g (k) is defined not only by the dispersion relation ω(k), but also by other elements of the initial problem. As applied to the dissipative medium, it is shown that v _g (k) defines the field energy transfer velocity, and this velocity does not exceed thee light speed in vacuum. An expression for the energy transfer velocity is also obtained for the case where the dispersion relation is given in the form k = k′(ω) + ik″(ω) which corresponds to the boundary problem.     

Testing the Distance-Duality Relation from Hubble,Galaxy Clusters and Type Ia Supernovae Data with Model Independent Methods

In this paper, we perform cosmological-model-independent tests for the distance-duality (DD) relation η(z)=D _L(1+z)^?2/D _A by combining the angular diameter distance D _A(or comoving distances D _c ) with the luminosity distance D _L. The D _A are provided by two galaxy clusters samples compiled by De Filippis et al. (the elliptical β model), Bonamente et al. (the spherical β model), the D _c are obtained from Hubble parameter data and D _L are given from the Union2.1 supernovae (SNe) Ia compilation. We employ two methods, i.e., method A: binning the SNe Ia data within the range Δz=|z?z _SNe|<0.005, and method B: reconstructing the D _L(z) by smoothing the noise of Union2.1 data set over redshift with the Gaussian smoothing function, to obtain D _L associated with the redshits of the observed D _A or D _c. Four parameterizations for η(z), i.e., η(z)=1+η ₀ z, η(z)=1+η ₀ z/(1+z), η(z)=1+η ₀ z/(1+z)² and η(z)=1?η ₀ ln(1+z), are adopted for the DD relation. We find that DD relation is consistent with the present observational data, and the results we obtained are not sensitive to the method and parameterization.     

Probing the sign-changeable interaction between dark energy and dark matter with current observations

We consider the models of vacuum energy interacting with cold dark matter in this study, in which the coupling can change sigh during the cosmological evolution. We parameterize the running coupling b by the form b(a) = b_0 a + b_e(1-a), where at the earlytime the coupling is given by a constant b_e and today the coupling is described by another constant b_0. We explore six specific models with(i) Q = b(a)H_0ρ_0,(ii) Q = b(a)H_0ρ_(de),(iii) Q = b(a)H_0ρ_c,(iv) Q = b(a)Hρ_0,(v) Q = b(a)Hρ_(de), and(vi) Q = b(a)Hρ_c.The current observational data sets we use to constrain the models include the JLA compilation of type Ia supernova data, the Planck 2015 distance priors data of cosmic microwave background observation, the baryon acoustic oscillations measurements,and the Hubble constant direct measurement. We find that, for all the models, we have b_0 0 and b_e 0 at around the 1σ level,and b_0 and b_e are in extremely strong anti-correlation. Our results show that the coupling changes sign during the evolution at about the 1σ level, i.e., the energy transfer is from dark matter to dark energy when dark matter dominates the universe and the energy transfer is from dark energy to dark matter when dark energy dominates the universe.     

Effect of the Lattice and Spin-Phonon Contributions on the Temperature Behavior of the Ground State Splitting of Gd<Superscript>3+</Superscript> in SrMoO<Subscript>4</Subscript>

The temperature behavior of the EPR spectra of the Gd³⁺ impurity center in single crystals of SrMoO₄ in the temperature range T = 99–375 K is studied. The analysis of the temperature dependences of the spin Hamiltonian b ₂ ⁰ (T) = b₂(F) + b₂(L) and P ₂ ⁰ (T) = P₂(F) + P₂(L) (for Gd¹⁵⁷) describing the EPR spectrum and contributing to the Gd³⁺ ground state splitting ΔE is carried out. In terms of the Newman model, the values of b₂(L) and P₂(L) depending on the thermal expansion of the static lattice are estimated; the b₂(F) and P₂(F) spin-phonon contributions determined by the lattice ion oscillations are separated. The analysis of b ₂ ⁰ (T) and P ₂ ⁰ (T) is evidence of the positive contribution of the spin-phonon interaction; the model of the local oscillations of the impurity cluster with close frequencies ω describes well the temperature behavior of b₂(F) and P₂(F).     

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).     

Thermodynamic study of compounds of the Nd-Ba-Cu-O system

Standard enthalpies of formation for solid solutions of composition Nd_{1 + x} Ba_{2 ? x} Cu₃O _y (x = 0–0.8, y = 6.65–7.24) from oxides were determined by solution calorimetry. The heat capacity of NdBa₂Cu₃O_6.87 phase was measured in the range 5–320 K by low-temperature adiabatic calorimetry. The absolute entropy S ^o(T), the difference of enthalpies H ^o(T)-H ^o(0 K), and the reduced Gibbs energy Φ^o(T) = S ^o(T)–[H ^o(T)–H ^o(0)]/T were calculated on the basis of smoothed dependence C _p (T) in the 0–320 K range. An assessment was made for the heat capacities and the absolute entropies of solid solutions Nd_1+x Ba_2?x Cu₃O _y . The obtained set of thermodynamic parameters can be used for the calculation of phase equilibria in the Nd-Ba-Cu-O system.     

Electro-optical properties of strontium-barium niobate crystals and their relation to the domain structure of the crystals

The electro-optical coefficients r _ij and half-wave voltage V_λ/2 of strontium-barium niobate crystals poled in the ferroelectric phase are shown to vary along the polar axis. The r _ij (z) and V_λ/2(z) dependences indicate the presence of a residual domain density D(z) and clearly depend on the sign of the polarizing field, with r _ij being minimum (D being maximum) near the negative electrode. This character of the D(z) distribution and, hence, the r _ij (z) and V_λ/2(z) coordinate dependences can be explained by predominant domain nucleation near the negative electrode, which is revealed when the switching processes are studied using 90° (Rayleigh) light scattering from domain walls.     

Exact expressions for the energy current and stress tensor operators in many-particle systems

For some purposes in statistical physics, such as, for example, the calculation of various transport coefficients, it is necessary to have expressions for the energy current operatorS and stress tensor operatorT _lm . In this work it is shown that by using a simple identity, exact expressions forS andT _lm which satisfy the conservation laws for the energy density? and momentum densityP, respectively, exist.S andT _lm can each be written as a sum of two parts,S=S ^(A) +S ^(B) T _lm =T _lm ^(A) +T _lm ^(B) . The “A” part is the ordinary convective or kinetic part while the “B” part is shown to be expressible as a gradient and hence its homogeneous component vanishes identically. The expressions are compared with approximate forms found in the literature. The operators are Fourier analyzed and written in terms of the field operators in the second quantization formalism.     

On the nature of the liquid-to-glass transition equation

Within the model of delocalized atoms, it is shown that the parameter δT_g, which enters the glasstransition equation qτ_g = δT_g and characterizes the temperature interval in which the structure of a liquid is frozen, is determined by the fluctuation volume fraction \({f_g} = {\left( {{{\Delta {V_e}} \mathord{\left/ {\vphantom {{\Delta {V_e}} V}} \right. \kern-\nulldelimiterspace} V}} \right)_{T = {T_g}}}\) frozen at the glass-transition temperature T_g and the temperature T_g itself. The parameter δT_g is estimated by data on f_g and T_g. The results obtained are in agreement with the values of δT_g calculated by the Williams–Landel–Ferry (WLF) equation, as well as with the product qτ_g—the left-hand side of the glass-transition equation (q is the cooling rate of the melt, and τ_g is the structural relaxation time at the glass-transition temperature). Glasses of the same class with f_g ≈ const exhibit a linear correlation between δT_g and T_g. It is established that the currently used methods of Bartenev and Nemilov for calculating δT_g yield overestimated values, which is associated with the assumption, made during deriving the calculation formulas, that the activation energy of the glass-transition process is constant. A generalized Bartenev equation is derived for the dependence of the glass-transition temperature on the cooling rate of the melt with regard to the temperature dependence of the activation energy of the glasstransition process. A modified version of the kinetic glass-transition criterion is proposed. A conception is developed that the fluctuation volume fraction f = ΔV_e/V can be interpreted as an internal structural parameter analogous to the parameter ξ in the Mandelstam–Leontovich theory, and a conjecture is put forward that the delocalization of an active atom—its critical displacement from the equilibrium position—can be considered as one of possible variants of excitation of a particle in the Vol’kenshtein–Ptitsyn theory. The experimental data used in the study refer to a constant cooling rate of q = 0.05 K/s (3 K/min).     

High precision determination of the low-energy constants for the two-dimensional quantum Heisenberg model on the honeycomb lattice

The low-energy constants, namely the staggered magnetization density M? _s per spin, the spin stiffness ρ _s , and the spinwave velocity c of the two-dimensional (2-d) spin-1/2 Heisenberg model on the honeycomb lattice are calculated using first principles Monte Carlo method. The spinwave velocity c is determined first through the winding numbers squared. M? _s and ρ _s are then obtained by employing the relevant volume- and temperature-dependence predictions from magnon chiral perturbation theory. The periodic boundary conditions (PBCs) implemented in our simulations lead to a honeycomb lattice covering both a rectangular and a parallelogram-shaped region. Remarkably, by appropriately utilizing the predictions of magnon chiral perturbation theory, the numerical values of M? _s , ρ _s , and c we obtain for both the considered periodic honeycomb lattice of different geometries are consistent with each other quantitatively. The numerical accuracy reached here is greatly improved. Specifically, by simulating the 2-d quantum Heisenberg model on the periodic honeycomb lattice overlaying a rectangular area, we arrive at M? _s = 0.26882(3), ρ _s  = 0.1012(2)J, and c = 1.2905(8)Ja. The results we obtain provide a useful lesson for some studies such as simulating fermion actions on hyperdiamond lattice and investigating second order phase transitions with twisted boundary conditions.     

Forced snaking: Localized structures in the real Ginzburg-Landau equation with spatially periodic parametric forcing

We study spatial localization in the real subcritical Ginzburg-Landau equation u _t = m ₀ u + Q(x)u + u _xx + d|u|² u ?|u|⁴ u with spatially periodic forcing Q(x). When d>0 and Q ≡ 0 this equation exhibits bistability between the trivial state u = 0 and a homogeneous nontrivial state u = u ₀ with stationary localized structures which accumulate at the Maxwell point m ₀ = ?3d ²/16. When spatial forcing is included its wavelength is imprinted on u ₀ creating conditions favorable to front pinning and hence spatial localization. We use numerical continuation to show that under appropriate conditions such forcing generates a sequence of localized states organized within a snakes-and-ladders structure centered on the Maxwell point, and refer to this phenomenon as forced snaking. We determine the stability properties of these states and show that longer lengthscale forcing leads to stationary trains consisting of a finite number of strongly localized, weakly interacting pulses exhibiting foliated snaking.     

Variations in thermal properties of diamond under isothermal compression

State equation P(V/V ₀, T) and baric dependences of thermal properties of diamond have been obtained without any fitting parameters from the interatomic pair Mie–Lennard-Jones potential and the Einstein model of a crystal. Calculations have been performed along two isotherms (at T = 300 and 3000 K) up to P = 10000 kbar = 1000 GPa, i.e., to a relative volume of V/V ₀ = 0.5. The baric dependences have been obtained for the following characteristics: isothermal elastic modulus B _T and B'(P), isochoric heat capacity C _v and C _v ' (P), isobaric heat capacity C _p ; thermal expansion coefficient α _p and α _p ' (P); and specific surface energy σ, as well as its derivatives σ'(P) and σ'(T). It is shown that for P → ∞, functions B _T (P) and σ(P) vary linearly, functions B'(P), α _p (P), C _v (P), C _p (P) and σ'(P) tend to constants, while functions α _p '(P), C _v '(P), and difference C _p (P)–C _v (P) tend to zero. Good agreement with experimental data has been demonstrated.