On gauge-invariant Green function in 2+1 dimensional QED

Both the gauge-invariant fermion Green function and gauge-dependent conventional Green function in $2+1$ dimensional QED are studied in the large $N$ limit. In temporal gauge, the infra-red divergence of gauge-dependent Green function is found to be regulariable, the anomalous dimension is found to be $\eta= \frac{64}{3 \pi^{2} N}$. This anomalous dimension was argued to be the same as that of gauge-invariant Green function. However, in Coulomb gauge, the infra-red divergence of the gauge-dependent Green function is found to be un-regulariable, anomalous dimension is even not defined, but the infra-red divergence is shown to be cancelled in any gauge-invariant physical quantities. The gauge-invariant Green function is also studied directly in Lorentz covariant gauge and the anomalous dimension is found to be the same as that calculated in temporal gauge.Comment: 8 pages, 6 figures, to appear in Phys. Rev.

THE MACROKINETICS PARAMETERS OF THE HYDROCARBONS COMBUSTION IN THE NUMERICAL CALCULATION OF ACCIDENTAL EXPLOSIONS IN MINES

Purpose. Obtaining effective parameters of the macrokinetics of combustion of hydrocarbons in the deflagration and detonation regime for the numerical calculation of emergency explosions in mine workings. Methodology. Mathematical modeling, numerical experiment, kinetics analysis of explosive combustion reaction, analysis and synthesis. Findings. The paper analyzes the parameters of the kinetic equation against experimental data. Obtaining such data in a physical experiment for explosive chemical reactions meets serious difficulties. This is due to the size of the reaction zone not exceeding fractions of a millimeter, the lack of time resolution of experimental techniques and other factors leading to errors in direct measurements and the emergence of multiple solutions. This possibility contributes to obtaining a simultaneous numerical solution of the equations of gas dynamics and chemical kinetics. In the numerical experiment, a direct relationship between the macrokinetic characteristics of the chemical reaction and the parameters of the discontinuous flow of the reacting gas stream is established: velocity, pressure in the front and behind the front of the detonation and deflagration wave. Based on this, Arrhenius characteristics of the reaction – preexponential and effective activation energy for the hydrocarbons under consideration are obtained. Originality. Macrokinetic parameters are established for simulating one-stage ignition and burning of the most probable hydrocarbons of the mine atmosphere in the deflagration and detonation regime. Modeling of explosive combustion of premixed hydrocarbons in stoichiometric concentrations is performed. It is shown that the values of the effective activation energy in explosive combustion reactions are of less importance in contrast to steady-state combustion reactions because of the effect of the gas-dynamical effects of the shock wave on the reaction rate. The Arrhenius characteristics of the reaction – the pre-exponential and the effective activation energy – have been agreed upon, according to the gas dynamic and kinetic parameters of the course of the explosive combustion reaction. Practical value. The obtained parameters of the macrokinetics of the explosive combustion reaction make it possible to apply simple kinetic mechanisms in practical calculations of the processes of deflagration and detonation combustion, and to predict the parameters of emergency explosions in conditions of mine workings with sufficient accuracy. This also makes it possible to solve the problem of accounting for the presence of heavy hydrocarbons in themine atmosphere as products of coal pyrolysis in underground fires as factors of increasing the risk of emergency explosions

Fractional exclusion and braid statistics in one dimension: a study via dimensional reduction of Chern-Simons theory

The relation between braid and exclusion statistics is examined in one-dimensional systems, within the framework of Chern-Simons statistical transmutation in gauge invariant form with an appropriate dimensional reduction. If the matter action is anomalous, as for chiral fermions, a relation between braid and exclusion statistics can be established explicitly for both mutual and nonmutual cases. However, if it is not anomalous, the exclusion statistics of emergent low energy excitations is not necessarily connected to the braid statistics of the physical charged fields of the system. Finally, we also discuss the bosonization of one-dimensional anyonic systems through T-duality.Comment: 19 pages, fix typo

Monoclinic phase in the relaxor-based piezo-/ ferroelectric Pb(Mg1/3_{1/3}Nb2/3)O3_{2/3})O_3-PbTiO3_3 system

A ferroelectric monoclinic phase of space group $Cm$ ($M_A$ type) has been discovered in 0.65Pb(Mg$_{1/3}$Nb$_{2/3})O_3$-0.35PbTiO$_3$ by means of high resolution synchrotron X-ray diffraction. It appears at room temperature in a single crystal previously poled under an electric field of 43 kV/cm applied along the pseudocubic [001] direction, in the region of the phase diagram around the morphotropic phase boundary between the rhombohedral (R3m) and the tetragonal (P4mm) phases. The monoclinic phase has lattice parameters a = 5.692 A, b = 5.679 A, c = 4.050 A and $\beta$ = $90.15^{\circ}$, with the b$_m$-axis oriented along the pseudo-cubic [110] direction . It is similar to the monoclinic phase observed in PbZr$_{1-x}$Ti$_x$O$_3$, but different from that recently found in Pb(Zn$_{1/3}$Nb$_{2/3})O_3$-PbTiO$_3$, which is of space group $Pm$ ($M_C$ type).Comment: Revised version after referees' comments. PDF file. 6 pages, 4 figures embedde

Gauge-invariant Green function in 3+1 dimensional QED (QCD) and 2+1 dimensional Abelian (Non-Abelian) Chern-Simon theory

By applying the simple and effective method developed to study the the gauge-invariant fermion Green function in $2+1$ dimensional non-compact QED, we study the gauge-invariant Green function in $3+1$ dimensional QED and $2+1$ dimensional non-compact Chern-Simon theory. We also extend our results to the corresponding $SU(M)$ non-Abelian gauge theories. Implications for Fractional Quantum Hall effect are briefly discussed.Comment: 8 pages, 4 figures, published versio

Momentum Distribution of Near-Zero-Energy Photoelectrons in the Strong-Field Tunneling Ionization in the Long Wavelength Limit

We investigate the ionization dynamics of Argon atoms irradiated by an ultrashort intense laser of a wavelength up to 3100 nm, addressing the momentum distribution of the photoelectrons with near-zero-energy. We find a surprising accumulation in the momentum distribution corresponding to meV energy and a \textquotedblleft V"-like structure at the slightly larger transverse momenta. Semiclassical simulations indicate the crucial role of the Coulomb attraction between the escaping electron and the remaining ion at extremely large distance. Tracing back classical trajectories, we find the tunneling electrons born in a certain window of the field phase and transverse velocity are responsible for the striking accumulation. Our theoretical results are consistent with recent meV-resolved high-precision measurements.Comment: 5 pages, 4 figure

Vortex -- Kink Interaction and Capillary Waves in a Vector Superfluid

Interaction of a vortex in a circularly polarized superfluid component of a 2d complex vector field with the phase boundary between superfluid phases with opposite signs of polarization leads to a resonant excitation of a ``capillary'' wave on the boundary. This leads to energy losses by the vortex--image pair that has to cause its eventual annihilation.Comment: LaTeX 7 pages, no figure