On the Hamiltonian form of the Einstein equations for gravitational field

It is shown that Einstein gravitational equations and canonical equations following from the Dirac-Schwinger Hamiltonian in the Faddeev variables coincide. For proving of this at first, the Einstein equations has been rewritten in canonical variables, and after this, the time derivative of the generalized momenta of the gravitational field in Faddeev form has been calculated using canonical Poisson brackets. The results coincide.Comment: 7 page

Towards higher-order calculations of quarkonia production with kTk_T-factorization: PP-wave charmonia

Inclusive $P$-wave charmonia production in hadronic collisions at high energies is discussed in the framework of non-relativistic QCD and $k_T$-factorization formalism. We present two consistent approches to merge the usual leading order $k_T$-factorization calculations with tree-level next-to-leading order off-shell amplitudes. Using these prescriptions, we extracted long-distance matrix elements for $\chi_c$ mesons from a combined fit to available Tevatron and LHC data. In contrast to previous (leading order) calculations, our fits do not contradict equal color singlet wave functions of $\chi_{c1}$ and $\chi_{c2}$ states. The extracted values of long-distance matrix elements are employed to analyse the $\chi_c$ polarization data reported recently by the CMS Collaboration. Our predictions are in a reasonably good agreement with the Tevatron and LHC measurements within the theoretical and experimental uncertainties.Comment: 23 pages, 11 figures, 1 tabl

Revisiting the production of J/ψJ/\psi pairs at the LHC

We consider the prompt double $J/\psi$ production in $pp$ collisions at the LHC in the framework of $k_T$-factorization QCD approach. Using the fragmentation mechanism, we evaluate the color octet contributions to the production cross sections taking into account the combinatorial effects of multiple gluon radiation in the initial state driven by the Ciafaloni-Catani-Fiorani-Marchesini evolution equation. We demonstrate the importance of these contributions in a certain kinematical region covered by the CMS and ATLAS measurements. On the other hand, the experimental data taken by the LHCb Collaboration at forward rapidities and moderate transverse momenta can be described well by ${\cal O}(\alpha_s^4)$ color singlet terms and contributions from the double parton scattering mechanism. The extracted value of the effective cross section $\sigma_{\rm eff} = 17.5 \pm 4.1$~mb is compatible with many other estimations based on different final states.Comment: 18 pages, 10 figure

B-T phase diagram of CoCr2O4 in magnetic fields up to 14 T

We have measured the magnetization and specific heat of multiferroic CoCr2O4 in magnetic fields up to 14 T. The high-field magnetization measurements indicate a new phase transition at T* = 5 - 6 K. The phase between T* and the lock-in transition at 15 K is characterized by magnetic irreversibility. At higher magnetic fields, the irreversibility increases. Specific-heat measurements confirm the transition at T*, and also show irreversible behavior. We construct a field-temperature phase diagram of CoCr2O4.Comment: 4 page

Metastable phases and "metastable" phase diagrams

The work discusses specifics of phase transitions for metastable states of substances. The objects of condensed media physics are primarily equilibrium states of substances with metastable phases viewed as an exception, while the overwhelming majority of organic substances investigated in chemistry are metastable. It turns out that at normal pressure many of simple molecular compounds based on light elements (these include: most hydrocarbons; nitrogen oxides, hydrates, and carbides; carbon oxide (CO); alcohols, glycerin etc) are metastable substances too, i.e. they do not match the Gibbs' free energy minimum for a given chemical composition. At moderate temperatures and pressures, the phase transitions for given metastable phases throughout the entire experimentally accessible time range are reversible with the equilibrium thermodynamics laws obeyed. At sufficiently high pressures (1-10 GPa), most of molecular phases irreversibly transform to more energy efficient polymerized phases, both stable and metastable. These transformations are not consistent with the equality of the Gibbs' free energies between the phases before and after the transition, i.e. they are not phase transitions in "classical" meaning. The resulting polymeric phases at normal pressure can exist at temperatures above the melting one for the initial metastable molecular phase. Striking examples of such polymers are polyethylene and a polymerized modification of CO. Many of energy-intermediate polymeric phases can apparently be synthesized by the "classical" chemistry techniques at normal pressure.Comment: 5 pages, 4 figure

Uncertainty relations in curved spaces

Uncertainty relations for particle motion in curved spaces are discussed. The relations are shown to be topologically invariant. New coordinate system on a sphere appropriate to the problem is proposed. The case of a sphere is considered in details. The investigation can be of interest for string and brane theory, solid state physics (quantum wires) and quantum optics.Comment: published version; phase space structure discussion adde

Probing the ground state in gauge theories

We consider two very different models of the flux tube linking two heavy quarks: a string linking the matter fields and a Coulombic description of two separately gauge invariant charges. We compare how close they are to the unknown true ground state in compact U(1) and the SU(2) Higgs model. Simulations in compact U(1) show that the string description is better in the confined phase but the Coulombic description is best in the deconfined phase; the last result is shown to agree with analytical calculations. Surprisingly in the non-abelian theory the Coulombic description is better in both the Higgs and confined phases. This indicates a significant difference in the width of the flux tubes in the two theories.Comment: 13 pages, 10 .eps figures. V2: conclusions extende

The Cauchy convergence of T and P-approximant templates for test-mass Kerr binary systems

In this work we examine the Cauchy convergence of both post-Newtonian (T-approximant) and re-summed post-Newtonian (P-approximant) templates for the case of a test-mass orbiting a Kerr black hole along a circular equatorial orbit. The Cauchy criterion demands that the inner product between the $n$ and $n+1$ order approximation approaches unity, as we increase the order of approximation. In previous works, it has been shown that we achieve greater fitting factors and better parameter estimation using the P-approximant templates for both Schwarzschild and Kerr black holes. In this work, we show that the P-approximant templates also display a faster Cauchy convergence making them a superior template to the standard post-Newtonian templates.Comment: 5 pages, Replaced with shortened published versio