Gell-Mann - Low Function in QED for the arbitrary coupling constant

The Gell-Mann -- Low function \beta(g) in QED (g is the fine structure constant) is reconstructed. At large g, it behaves as \beta_\infty g^\alpha with \alpha\approx 1, \beta_\infty\approx 1.Comment: 5 pages, PD

Quantum Electrodynamics at Extremely Small Distances

The asymptotics of the Gell-Mann - Low function in QED can be determined exactly, \beta(g)= g at g\to\infty, where g=e^2 is the running fine structure constant. It solves the problem of pure QED at small distances L and gives the behavior g\sim L^{-2}.Comment: Latex, 6 pages, 1 figure include

Reducing digger energy consumption by improving the walking mechanism

To evaluate the energy to move the excavator body, we calculated the effort involved in the hydraulic cylinders of the walking mechanism. Unlike man, "pacing" the excavator is on a "drawing", in which the housing pulls the excavator walking mechanism in the direction of the reference points. As a result, the kinematic and dynamic study of the process of pacing is reduced to the analysis of speeds and loads for the simplest of mechanisms, known since ancient times as the slider-crank mechanism. Analysis of the motion of this mechanism can be carried out by conventional (calculated for one position) or by modern analytical methods. Modern methods of analytical studies of the mechanisms permit a computer calculation of the full cycle of movement of the excavator in a single step and to evaluate the stresses produced in the hydraulic cylinders. A variety of design solutions based on different positions of the connecting joints is recorded during the test set kinematics and, accordingly, an amount in the results is obtained. Power movement by one step excavator is theoretically estimated as the amount of work the forces acting on the mechanism during this step undertake. A design that corresponds to the minimum energy consumption should be considered optimal for this type of walking mechanism. The authors of this paper analyzed the performing over thirty different types of mechanisms of pacing. Recommendations for optimizing their designs are formulated for each of these, which not only reduces the power consumption excavator, but also reduces its price. © 2014 WIT Press

Spin Polarization Phenomena and Pseudospin Quantum Hall Ferromagnetism in the HgTe Quantum Well

The parallel field of a full spin polarization of the electron gas in a \Gamma8 conduction band of the HgTe quantum well was obtained from the magnetoresistance by three different ways in a zero and quasi-classical range of perpendicular field component Bper. In the quantum Hall range of Bper the spin polarization manifests in anticrossings of magnetic levels, which were found to strongly nonmonotonously depend on Bper.Comment: to be published in AIP Conf. Proc.: 15-th International Conference on Narrow Gap Systems (NGS-15

Finite-size scaling from self-consistent theory of localization

Accepting validity of self-consistent theory of localization by Vollhardt and Woelfle, we derive the finite-size scaling procedure used for studies of the critical behavior in d-dimensional case and based on the use of auxiliary quasi-1D systems. The obtained scaling functions for d=2 and d=3 are in good agreement with numerical results: it signifies the absence of essential contradictions with the Vollhardt and Woelfle theory on the level of raw data. The results \nu=1.3-1.6, usually obtained at d=3 for the critical exponent of the correlation length, are explained by the fact that dependence L+L_0 with L_0>0 (L is the transversal size of the system) is interpreted as L^{1/\nu} with \nu>1. For dimensions d\ge 4, the modified scaling relations are derived; it demonstrates incorrectness of the conventional treatment of data for d=4 and d=5, but establishes the constructive procedure for such a treatment. Consequences for other variants of finite-size scaling are discussed.Comment: Latex, 23 pages, figures included; additional Fig.8 is added with high precision data by Kramer et a

Analytical realization of finite-size scaling for Anderson localization. Does the band of critical states exist for d>2?

An analytical realization is suggested for the finite-size scaling algorithm based on the consideration of auxiliary quasi-1D systems. Comparison of the obtained analytical results with the results of numerical calculations indicates that the Anderson transition point is splitted into the band of critical states. This conclusion is supported by direct numerical evidence (Edwards and Thouless, 1972; Last and Thouless, 1974; Schreiber, 1985; 1990). The possibility of restoring the conventional picture still exists but requires a radical reinterpretetion of the raw numerical data.Comment: PDF, 11 page

Scaling near the upper critical dimensionality in the localization theory

The phenomenon of upper critical dimensionality d_c2 has been studied from the viewpoint of the scaling concepts. The Thouless number g(L) is not the only essential variable in scale transformations, because there is the second parameter connected with the off-diagonal disorder. The investigation of the resulting two-parameter scaling has revealed two scenarios, and the switching from one to another scenario determines the upper critical dimensionality. The first scenario corresponds to the conventional one-parameter scaling and is characterized by the parameter g(L) invariant under scale transformations when the system is at the critical point. In the second scenario, the Thouless number g(L) grows at the critical point as L^{d-d_c2}. This leads to violation of the Wegner relation s=\nu(d-2) between the critical exponents for conductivity (s) and for localization radius (\nu), which takes the form s=\nu(d_c2-2). The resulting formulas for g(L) are in agreement with the symmetry theory suggested previously [JETP 81, 925 (1995)]. A more rigorous version of Mott's argument concerning localization due topological disorder has been proposed.Comment: PDF, 7 pages, 6 figure

Renormalization Group Functions for Two-Dimensional Phase Transitions: To the Problem of Singular Contributions

According to the available publications, the field theoretical renormalization group (RG) approach in the two-dimensional case gives the critical exponents that differ from the known exact values. This fact was attempted to explain by the existence of nonanalytic contributions in the RG functions. The situation is analysed in this work using a new algorithm for summing divergent series that makes it possible to analyse dependence of the results for the critical exponents on the expansion coefficients for RG functions. It has been shown that the exact values of all the exponents can be obtained with a reasonable form of the coefficient functions. These functions have small nonmonotonities or inflections, which are poorly reproduced in natural interpolations. It is not necessary to assume the existence of singular contributions in RG functions.Comment: PDF, 11 page