On the Three-dimensional Lattice Model

Using the restricted star-triangle relation, it is shown that the $N$-state spin integrable model on a three-dimensional lattice with spins interacting round each elementary cube of the lattice proposed by Mangazeev, Sergeev and Stroganov is a particular case of the Bazhanov-Baxter model.Comment: 8 pages, latex, 4 figure

Empirical Parameterization of Nucleon-Nucleon Elastic Scattering Amplitude at High Beam Momenta for Glauber Calculations and Monte Carlo Simulations

A parameterization of the nucleon-nucleon elastic scattering amplitude is needed for future experiments with nucleon and nuclear beams in the beam momentum range of 2 -- 50 GeV/c/nucleon. There are many parameterizations of the amplitude at $P_{lab} >$ 25--50 GeV/c, and at $P_{lab} \leq$ 5 GeV/c. Our paper is aimed to cover the range between 5 -- 50 GeV/c. The amplitude is used in Glauber calculations of various cross sections and Monte Carlo simulations of nucleon-nucleon scatterings. Usually, the differential nucleon-nucleon elastic scattering cross sections are described by an exponential expression. Corresponding experimental data on $pp$ interactions at $|t|>$ 0.005 (GeV/c)$^2$ and $|t|\leq$ 0.125 (GeV/c)$^2$ have been fit. We propose formulae to approximate the beam momentum dependence of these parameters in the momentum range considered. The same was done for $np$ interactions at $|t|\leq$ 0.5 (GeV/c)$^2$. Expressions for the momentum dependence of the total and elastic cross sections, and the ratio of real to imaginary parts of the amplitude at zero momentum transfer are also given for $pp$ and $np$ collisions. These results are sufficient for a first approximation of the Glauber calculations. For more exact calculations we fit the data at $|t|>$ 0.005 (GeV/c)$^2$ without restrictions on the maximum value of $|t|$ using an expression based on two coherent exponential. The parameters of the fits are found for the beam momentum range 2 -- 50 GeV/c.Comment: 14 pages, 10 figure

XAFS spectroscopy. I. Extracting the fine structure from the absorption spectra

Three independent techniques are used to separate fine structure from the absorption spectra, the background function in which is approximated by (i) smoothing spline. We propose a new reliable criterion for determination of smoothing parameter and the method for raising of stability with respect to k_min variation; (ii) interpolation spline with the varied knots; (iii) the line obtained from bayesian smoothing. This methods considers various prior information and includes a natural way to determine the errors of XAFS extraction. Particular attention has been given to the estimation of uncertainties in XAFS data. Experimental noise is shown to be essentially smaller than the errors of the background approximation, and it is the latter that determines the variances of structural parameters in subsequent fitting.Comment: 16 pages, 7 figures, for freeware XAFS analysis program, see http://www.crosswinds.net/~klmn/viper.htm

Domain walls of ferroelectric BaTiO3 within the Ginzburg-Landau-Devonshire phenomenological model

Mechanically compatible and electrically neutral domain walls in tetragonal, orthorhombic and rhombohedral ferroelectric phases of BaTiO3 are systematically investigated in the framework of the phenomenological Ginzburg-Landau-Devonshire (GLD) model with parameters of Ref. [Hlinka and Marton, Phys. Rev. 74, 104104 (2006)]. Polarization and strain profiles within domain walls are calculated numerically and within an approximation leading to the quasi-one-dimensional analytic solutions applied previously to the ferroelectric walls of the tetragonal phase [W. Cao and L.E. Cross, Phys. Rev. 44, 5 (1991)]. Domain wall thicknesses and energy densities are estimated for all mechanically compatible and electrically neutral domain wall species in the entire temperature range of ferroelectric phases. The model suggests that the lowest energy walls in the orthorhombic phase of BaTiO3 are the 90-degree and 60-degree walls. In the rhombohedral phase, the lowest energy walls are the 71-degree and 109-degree walls. All these ferroelastic walls have thickness below 1 nm except for the 90-degree wall in the tetragonal phase and the 60-degree S-wall in the orthorhombic phase, for which the larger thickness of the order of 5 nm was found. The antiparallel walls of the rhombohedral phase have largest energy and thus they are unlikely to occur. The calculation indicates that the lowest energy structure of the 109-degree wall and few other domain walls in the orthorhombic and rhombohedral phases resemble Bloch-like walls known from magnetism.Comment: 12 pages, 9 figure

Three-Dimensional Vertex Model in Statistical Mechanics, from Baxter-Bazhanov Model

We find that the Boltzmann weight of the three-dimensional Baxter-Bazhanov model is dependent on four spin variables which are the linear combinations of the spins on the corner sites of the cube and the Wu-Kadanoff duality between the cube and vertex type tetrahedron equations is obtained explicitly for the Baxter-Bazhanov model. Then a three-dimensional vertex model is obtained by considering the symmetry property of the weight function, which is corresponding to the three-dimensional Baxter-Bazhanov model. The vertex type weight function is parametrized as the dihedral angles between the rapidity planes connected with the cube. And we write down the symmetry relations of the weight functions under the actions of the symmetry group $G$ of the cube. The six angles with a constrained condition, appeared in the tetrahedron equation, can be regarded as the six spectrums connected with the six spaces in which the vertex type tetrahedron equation is defined.Comment: 29 pages, latex, 8 pasted figures (Page:22-29

Relativistic three-body recombination with the QED vacuum

Electron-positron pair annihilation into a single photon is studied when a second free electron is present. Focussing on the relativistic regime, we show that the photon emitted in the three-lepton interaction may exhibit distinct angular distributions and polarization properties. Moreover, the process can dominate over two-photon annihilation in relativistic electron-positron plasmas of few-MeV temperature. An analogy with three-body recombination of electrons with ions is drawn.Comment: 5 pages, 4 figure

The Cohomology of the Steendrod Algebra and Representations of the General Linear Groups

Let Tr_k be the algebraic transfer that maps from the coinvariants of certain GL_k-representation to the cohomology of the Steenrod algebra. This transfer was defined by W. Singer as an algebraic version of the geometrical transfer tr_k : pi_*^S((B[doublestrike V]_k)_+) --\u3e pi_*^S(S^0). It has been shown that the algebraic transfer is highly nontrivial, more precisely, that Tr_k is an isomorphism for k = 1, 2, 3 and that T_r = ⊕_k(Tr_k) is a homomorphism of algebras. In this paper, we first recognize the phenomenon that if we start from any degree d, and apply Sq^0 repeatedly at most (k- 2) times, then we get into the region, in which all the iterated squaring operations are isomorphisms on the coinvariants of the GL_k-representation. As a consequence, every finite Sq^0-family in the coinvariants has at most (k - 2) non zero elements. Two applications are exploited. The first main theorem is that Tr_k is not an isomorphism for k gte 5. Furthermore, Tr_k is not an isomorphism in infinitely many degrees for each k \u3e 5. We also show that if Tr_ell detects a nonzero element in certain degrees of Ker(Sq^0), then it is not a monomorphism and further, Tr_k is not a monomorphism in infinitely many degrees for each k \u3e ell. The second main theorem is that the elements of any Sq^0-family in the cohomology of the Steenrod algebra, except at most its first (k - 2) elements, are either all detected or all not detected by Tr_k, for every k. Applications of this study to the cases k = 4 and 5 show that Tr_4 does not detect the three families g, D_3, p\u27 and Tr_5 does not detect the family {h_(n+1)g_n|n gte 1}

Entangled Husimi distribution and Complex Wavelet transformation

Based on the proceding Letter [Int. J. Theor. Phys. 48, 1539 (2009)], we expand the relation between wavelet transformation and Husimi distribution function to the entangled case. We find that the optical complex wavelet transformation can be used to study the entangled Husimi distribution function in phase space theory of quantum optics. We prove that the entangled Husimi distribution function of a two-mode quantum state |phi> is just the modulus square of the complex wavelet transform of exp{-(|eta|^2)/2} with phi(eta)being the mother wavelet up to a Gaussian function.Comment: 7 page

Coal mine low power laser methane detection and alarm instrument

At present, the portable carrier catalytic methane detection and alarm instrument for coal mine generally has many problems, such as high power consumption, short standby time, low detection accuracy, few parameters and single function, which can not meet the rapid development needs of mine safety. In this paper, a low power portable laser methane detection and alarm instrument based on tunable laser absorption spectroscopy (TDLAS) is designed. The instrument can detect methane concentration, ambient temperature and ambient pressure at the same time. It has the functions of sound and light alarm, historical data storage and query, and integrates Wi-Fi to realize data wireless transmission. The instrument can work continuously for 36 hours, and the response time is less than 15 seconds. It has the function of self-diagnosis. The overall performance of the instrument has been greatly improved compared with the traditional mine methane portable instrument. A mobile methane alarm Internet of things(IOT) system for coal mine based on portable instrument has been developed, which realizes real-time upload of data and cloud analysis, makes the traditional mine gas monitoring and control system powerfully supplemented, greatly improves the detection level of coal mine gas, and has broad application prospects

Integrable impurities in Hubbard chain with the open boundary condition

The Kondo problem of two impurities in 1D strongly correlated electron system within the framework of the open boundary Hubbard chain is solved and the impurities, coupled to the ends of the electron system, are introduced by their scattering matrices with electrons so that the boundary matrices satisfy the reflecting integrability condition. The finite size correction of the ground state energy is obtained due to the impurities. Exact expressions for the low temperature specific heat contributed by the charge and spin parts of the magnetic impurities are derived. The Pauli susceptibility and the Kondo temperature are given explicitly. The Kondo temperature is inversely proportional to the density of electrons.Comment: 6 pages, Revtex, To appear in Europhysics Letter