Fractional Derivative as Fractional Power of Derivative

Definitions of fractional derivatives as fractional powers of derivative operators are suggested. The Taylor series and Fourier series are used to define fractional power of self-adjoint derivative operator. The Fourier integrals and Weyl quantization procedure are applied to derive the definition of fractional derivative operator. Fractional generalization of concept of stability is considered.Comment: 20 pages, LaTe

Phase-Space Metric for Non-Hamiltonian Systems

We consider an invariant skew-symmetric phase-space metric for non-Hamiltonian systems. We say that the metric is an invariant if the metric tensor field is an integral of motion. We derive the time-dependent skew-symmetric phase-space metric that satisfies the Jacobi identity. The example of non-Hamiltonian systems with linear friction term is considered.Comment: 12 page

Metal-insulator transition in a two-dimensional electron system: the orbital effect of in-plane magnetic field

The conductance of an open quench-disordered two-dimensional (2D) electron system subject to an in-plane magnetic field is calculated within the framework of conventional Fermi liquid theory applied to actually a three-dimensional system of spinless electrons confined to a highly anisotropic (planar) near-surface potential well. Using the calculation method suggested in this paper, the magnetic field piercing a finite range of infinitely long system of carriers is treated as introducing the additional highly non-local scatterer which separates the circuit thus modelled into three parts -- the system as such and two perfect leads. The transverse quantization spectrum of the inner part of the electron waveguide thus constructed can be effectively tuned by means of the magnetic field, even though the least transverse dimension of the waveguide is small compared to the magnetic length. The initially finite (metallic) value of the conductance, which is attributed to the existence of extended modes of the transverse quantization, decreases rapidly as the magnetic field grows. This decrease is due to the mode number reduction effect produced by the magnetic field. The closing of the last current-carrying mode, which is slightly sensitive to the disorder level, is suggested as the origin of the magnetic-field-driven metal-to-insulator transition widely observed in 2D systems.Comment: 19 pages, 7 eps figures, the extension of cond-mat/040613

"Unusual" metals in two dimensions: one-particle model of the metal-insulator transition at T=0

The conductance of disordered nano-wires at T=0 is calculated in one-particle approximation by reducing the original multi-dimensional problem for an open bounded system to a set of exactly one-dimensional non-Hermitian problems for mode propagators. Regarding two-dimensional conductor as a limiting case of three-dimensional disordered quantum waveguide, the metallic ground state is shown to result from its multi-modeness. On thinning the waveguide (in practice, e. g., by means of the ``pressing'' external electric field) the electron system undergoes a continuous phase transition from metallic to insulating state. The result predicted conform qualitatively to the observed anomalies of the resistance of different planar electron and hole systems.Comment: 7 pages, LATEX-2

Fractional Systems and Fractional Bogoliubov Hierarchy Equations

We consider the fractional generalizations of the phase volume, volume element and Poisson brackets. These generalizations lead us to the fractional analog of the phase space. We consider systems on this fractional phase space and fractional analogs of the Hamilton equations. The fractional generalization of the average value is suggested. The fractional analogs of the Bogoliubov hierarchy equations are derived from the fractional Liouville equation. We define the fractional reduced distribution functions. The fractional analog of the Vlasov equation and the Debye radius are considered.Comment: 12 page

A Complete Version of the Glauber Theory for Elementary Atom - Target Atom Scattering and Its Approximations

A general formalism of the Glauber theory for elementary atom (EA) - target atom (TA) scattering is developed. A second-order approximation of its complete version is considered in the framework of the optical-model perturbative approach. A `potential' approximation of a second-order optical model is formulated neglecting the excitation effects of the TA. Its accuracy is evaluated within the second-order approximation for the complete version of the Glauber EA-TA scattering theory.Comment: PDFLaTeX, 10 pages, no figures; an updated versio

Continuous Limit of Discrete Systems with Long-Range Interaction

Discrete systems with long-range interactions are considered. Continuous medium models as continuous limit of discrete chain system are defined. Long-range interactions of chain elements that give the fractional equations for the medium model are discussed. The chain equations of motion with long-range interaction are mapped into the continuum equation with the Riesz fractional derivative. We formulate the consistent definition of continuous limit for the systems with long-range interactions. In this paper, we consider a wide class of long-range interactions that give fractional medium equations in the continuous limit. The power-law interaction is a special case of this class.Comment: 23 pages, LaTe

Quantum properties of a non-Abelian gauge invariant action with a mass parameter

We continue the study of a local, gauge invariant Yang-Mills action containing a mass parameter, which we constructed in a previous paper starting from the nonlocal gauge invariant mass dimension two operator F_{\mu\nu} (D^2)^{-1} F_{\mu\nu}. We return briefly to the renormalizability of the model, which can be proven to all orders of perturbation theory by embedding it in a more general model with a larger symmetry content. We point out the existence of a nilpotent BRST symmetry. Although our action contains extra (anti)commuting tensor fields and coupling constants, we prove that our model in the limit of vanishing mass is equivalent with ordinary massless Yang-Mills theories. The full theory is renormalized explicitly at two loops in the MSbar scheme and all the renormalization group functions are presented. We end with some comments on the potential relevance of this gauge model for the issue of a dynamical gluon mass generation.Comment: 17 pages. v2: version accepted for publication in Phys.Rev.

Induction heating system for die tooling of press for isothermal stamping of large-sized parts

The paper describes the installation for stamping large-sized parts. The use of induction heating for heating the working tool of the stamp in the operating mode is considered. A system with 4 flat inductors is described. This solution allows for the most efficient hot stamping operation compared to other known solutions. An example of the result of numerical simulation of the temperature field distribution is demonstrated. © Published under licence by IOP Publishing Ltd.This work was financially supported by the Ministry of Science and Higher Education of the Russian Federation, project No. 075-11-2019-028

Observation of a narrow baryon resonance with positive strangeness formed in K+K^+Xe collisions

The charge-exchange reaction K^+ Xe --> K^0 p Xe' is investigated using the data of the DIANA experiment. The distribution of the pK^0 effective mass shows a prominent enhancement near 1538 MeV formed by \sim 80 events above the background, whose width is consistent with being entirely due to the experimental resolution. Under the selections based on a simulation of K^+Xe collisions, the statistical significance of the signal reaches 5.5\sigma. We interpret this observation as strong evidence for formation of a pentaquark baryon with positive strangeness, \Theta^+(uudd\bar{s}), in the charge-exchange reaction K^+ n --> K^0 p on a bound neutron. The mass of the \Theta^+ baryon is measured as m(\Theta^+) = 1538+-2 MeV. Using the ratio between the numbers of resonant and non-resonant charge-exchange events in the peak region, the intrinsic width of this baryon resonance is determined as \Gamma(\Theta^+) = 0.34+-0.10 MeV.Comment: 19 pages, 8 figure