Analytic calculation of field-strength correlators

Field correlators are expressed using background field formalism through the gluelump Green's functions. The latter are obtained in the path integral and Hamiltonian formalism. As a result behaviour of field correlators is obtained at small and large distances both for perturbative and nonperturbative parts. The latter decay exponentially at large distances and are finite at x=0, in agreement with OPE and lattice data.Comment: 28 pages, no figures; new material added, misprints correcte

Dynamics of confined gluons

Propagation of gluons in the confining vacuum is studied in the framework of the background perturbation theory, where nonperturbative background contains confining correlators. Two settings of the problem are considered. In the first the confined gluon is evolving in time together with static quark and antiquark forming the one-gluon static hybrid. The hybrid spectrum is calculated in terms of string tension and is in agreement with earlier analytic and lattice calculations. In the second setting the confined gluon is exchanged between quarks and the gluon Green's function is calculated, giving rise to the Coulomb potential modified at large distances. The resulting screening radius of 0.5 fm presents a serious problem when confronting with lattice and experimental data. A possible solution of this discrepancy is discussed.Comment: 17 pages, no figures; v2: minor numerical changes in the tabl

Solar neutrinos: the SNO salt phase results and physics of conversion

We have performed analysis of the solar neutrino data including results from the SNO salt phase as well as the combined analysis of the solar and the KamLAND results. The best fit values of neutrino parameters are Delta m^2 = 7.1e-5 eV^2, tan^2\theta = 0.40 with the boron flux f_B = 1.04. New SNO results strongly disfavor maximal mixing and the h-LMA region (Delta m^2 > 1e-4 eV^2) which is accepted now at the 3-sigma level. We find the 3-sigma upper bounds: Delta m^2 < 1.7e-4$ eV^2 and tan^2\theta < 0.64, and the lower bound Delta m^2 > 4.8e-5 eV^2. Non-zero 13-mixing does not change these results significantly. The present data determine quantitatively the physical picture of the solar neutrino conversion. At high energies relevant for SNO and Super-Kamiokande the deviation of the effective survival probability from the non-oscillatory value is about 10 - 14%. The oscillation effect contribution to this difference about 10% and the Earth regeneration is about 3 - 4%. At low energies (E < 1 MeV) the matter corrections to vacuum oscillation effect are below 5%. The predictions for the forthcoming measurements are given which include the spectral distortion and CC/NC ratio at SNO, the Day-Night asymmetry, the KamLAND spectrum and rate.Comment: figures and some numbers corrected, discussion of coherence loss added, number of pages slightly change

The matrix Hamiltonian for hadrons and the role of negative-energy components

The world-line (Fock-Feynman-Schwinger) representation is used for quarks in arbitrary (vacuum and valence gluon) field to construct the relativistic Hamiltonian. After averaging the Green's function of the white $q\bar q$ system over gluon fields one obtains the relativistic Hamiltonian, which is matrix in spin indices and contains both positive and negative quark energies. The role of the latter is studied in the example of the heavy-light meson and the standard einbein technic is extended to the case of the matrix Hamiltonian. Comparison with the Dirac equation shows a good agreement of the results. For arbitrary $q\bar q$ system the nondiagonal matrix Hamiltonian components are calculated through hyperfine interaction terms. A general discussion of the role of negative energy components is given in conclusion.Comment: 29 pages, no figure

Prediction of Atomization Energy Using Graph Kernel and Active Learning

Data-driven prediction of molecular properties presents unique challenges to the design of machine learning methods concerning data structure/dimensionality, symmetry adaption, and confidence management. In this paper, we present a kernel-based pipeline that can learn and predict the atomization energy of molecules with high accuracy. The framework employs Gaussian process regression to perform predictions based on the similarity between molecules, which is computed using the marginalized graph kernel. To apply the marginalized graph kernel, a spatial adjacency rule is first employed to convert molecules into graphs whose vertices and edges are labeled by elements and interatomic distances, respectively. We then derive formulas for the efficient evaluation of the kernel. Specific functional components for the marginalized graph kernel are proposed, while the effect of the associated hyperparameters on accuracy and predictive confidence are examined. We show that the graph kernel is particularly suitable for predicting extensive properties because its convolutional structure coincides with that of the covariance formula between sums of random variables. Using an active learning procedure, we demonstrate that the proposed method can achieve a mean absolute error of 0.62 +- 0.01 kcal/mol using as few as 2000 training samples on the QM7 data set

A model for Hopfions on the space-time S^3 x R

We construct static and time dependent exact soliton solutions for a theory of scalar fields taking values on a wide class of two dimensional target spaces, and defined on the four dimensional space-time S^3 x R. The construction is based on an ansatz built out of special coordinates on S^3. The requirement for finite energy introduces boundary conditions that determine an infinite discrete spectrum of frequencies for the oscillating solutions. For the case where the target space is the sphere S^2, we obtain static soliton solutions with non-trivial Hopf topological charges. In addition, such hopfions can oscillate in time, preserving their topological Hopf charge, with any of the frequencies belonging to that infinite discrete spectrum.Comment: Enlarged version with the time-dependent solutions explicitly given. One reference and two eps figures added. 14 pages, late

Pulsational instability of yellow hypergiants

Instability of population I (X=0.7, Y=0.02) massive stars against radial oscillations during the post-main sequence gravitational contraction of the helium core is investigated. Initial stellar masses are in the range from 65M_\odot to 90M_\odot. In hydrodynamic computations of self-exciting stellar oscillations we assumed that energy transfer in the envelope of the pulsating star is due to radiative heat conduction and convection. The convective heat transfer was treated in the framework of the theory of time-dependent turbulent convection. During evolutionary expansion of outer layers after hydrogen exhaustion in the stellar core the star is shown to be unstable against radial oscillations while its effective temperature is Teff > 6700K for Mzams=65M_\odot and Teff > 7200K for mzams=90M_\odot. Pulsational instability is due to the \kappa-mechanism in helium ionization zones and at lower effective temperature oscillations decay because of significantly increasing convection. The upper limit of the period of radial pulsations on this stage of evolution does not exceed 200 day. Radial oscillations of the hypergiant resume during evolutionary contraction of outer layers when the effective temperature is Teff > 7300K for Mzams=65M_\odot and Teff > 7600K for Mzams=90M_\odot. Initially radial oscillations are due to instability of the first overtone and transition to fundamental mode pulsations takes place at higher effective temperatures (Teff > 7700K for Mzams=65M_\odot and Teff > 8200K for Mzams=90M_\odot). The upper limit of the period of radial oscillations of evolving blueward yellow hypergiants does not exceed 130 day. Thus, yellow hypergiants are stable against radial stellar pulsations during the major part of their evolutionary stage.Comment: 20 pages, 7 gigures. Accepted for publication in Astronomy Letter