Renormalization group dependence of the QCD coupling

The general relation between the standard expansion coefficients and the beta function for the QCD coupling is exactly derived in a mathematically strict way. It is accordingly found that an infinite number of logarithmic terms are lost in the standard expansion with a finite order, and these lost terms can be given in a closed form. Numerical calculations, by a new matching-invariant coupling with the corresponding beta function to four-loop level, show that the new expansion converges much faster.     

Painlevé Representation of Tracy–Widom{_\beta} Distribution for {\beta} = 6

In Rumanov (J Math Phys 56:013508, 2015), we found explicit Lax pairs for the soft edge of beta ensembles with even integer values of \({\beta}\). Using this general result, the case \({\beta = 6}\) is further considered here. This is the smallest even \({\beta}\), when the corresponding Lax pair and its relation to Painlevé II (PII) have not been known before, unlike cases \({\beta = 2}\) and 4. It turns out that again everything can be expressed in terms of the Hastings–McLeod solution of PII. In particular, a second order nonlinear ordinary differential equation (ODE) for the logarithmic derivative of Tracy–Widom distribution for \({\beta = 6}\) involving the PII function in the coefficients is found, which allows one to compute asymptotics for the distribution function. The ODE is a consequence of a linear system of three ODEs for which the local singularity analysis yields series solutions with exponents in the set 4/3, 1/3 and ?2/3.     

Influence of coupling between junctions on breakpoint current in intrinsic Josephson junctions

We study theoretically the current-voltage characteristics of intrinsic Josephson junctions in high-Tc superconductors. An oscillation of the breakpoint current on the outermost branch as a function of coupling alpha and dissipation beta parameters is found. We explain this oscillation as a result of the creation of longitudinal plasma waves at the breakpoint with different wave numbers. We demonstrate the commensurability effect and predict a group behavior of the current-voltage characteristics for the stacks with a different number of junctions. A method to determine the wave number of longitudinal plasma waves from alpha and beta dependence of the breakpoint current is suggested. We model the alpha and beta dependence of the breakpoint current and obtain good agreement with the results of the simulation.     

Dielectric investigation of the temperature dependence of the nonexponentiality of the dynamics of polymer melts

Using broad band dielectric spectroscopy (10(-5)-10(9) Hz), combining time domain and frequency domain techniques, we study the temperature dependence of the non-Debye character of the alpha relaxation of polymer melts in the glass transition temperature T(g) range. The alpha relaxation process is described in terms of the Kohlrausch-Williams-Watts relaxation function which has a single parameter beta to characterize the nonexponentiality of the relaxation. At high temperatures, beta remains nearly insensitive to temperature changes, whereas in the vicinity of T(g) a nearly linear increasing of beta with temperature is found. The temperature range where the change of the beta(T) behavior occurs is located for all the polymers investigated around 1.2T(g). Moreover, our results indicate a common value of beta approximately equal to 1/3 at the temperature where the relaxation time diverges. The beta(T) behavior near T(g) is discussed in terms of a "rugged landscape" phase space which allows us to rationalize both the beta(T) behavior observed as well as the similarities of our findings near T(g) with the results reported in simulations on Ising spin glasses and other model systems.     

Gauge fixing and renormalization in topological quantum field theory

We show how Witten's topological Yang-Mills and gravitational quantum field theories may be obtained by a straightforward BRST gauge fixing procedure. We investigate some aspects of the renormalization of the topological Yang-Mills theory. It is found that the beta function for the Yang-Mills coupling constant is not zero.     

Derivation of the fine-structure formula utilizing the regularity properties of the Euler beta function

The method utilizing the integral Fourier transformation of the wave function of the ground state of the hydrogen-like atom is used to find its momentum representation, which is then used to derive the formula for the electron energy levels. Useful regularity properties are found for the Euler beta function appearing in the calculation of some formally diverging integrals. Smolensk State Pedagogical Institute. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 103–106, May, 1998.     

Fitting Chinese syllable-to-character mapping spectrum by the beta rank function

We define the syllable-to-character mapping spectrum in Chinese as the normalized number of characters per syllable ranked from high to low. This spectrum provides a statistical characterization of the relationship between spoken and written Chinese. We have shown that two functions, the logarithmic function and the beta rank function, fit the syllable-to-character mapping spectrum well. The beta rank function is even better than the logarithmic function judged by two measures of data-fitting performance: the sum of square errors, and Akaike information criterion. We comment on why the beta rank function is a good fitting function for many range-limited ranking data, whereas for range-open data it may be out-performed by other functions, such as a power-law function in the case of Zipf’s law.     

Reduced forms of the Wigner distribution function for the numerical analysis of rotationally symmetric synchrotron radiation

In an effort to provide a computationally convenient approach to the characterization of partially coherent synchrotron radiation in phase space, a thorough discussion of the minimum dimensionality of the Wigner distribution function for rotationally symmetric sources of arbitrary degrees of coherence is presented. It is found that perfectly coherent, perfectly incoherent and partially coherent sources may all be characterized by a three‐dimensional reduced Wigner distribution function, and some special cases are discussed in which a two‐dimensional reduced Wigner distribution function suffices. An application of the dimension‐reducing formalism to the case of partially coherent radiation from a planar undulator and a circularly symmetric electron beam as can be found in linear accelerators is demonstrated. The photon distribution is convolved over a realistic electron bunch, and how the beta function, emittance and energy spread of the bunch affect the total degree of coherence of the radiation is inspected. Finally the cross spectral density is diagonalized and the eigenmodes of the partially coherent radiation are recovered.     

Behavior of the beta function in SU(2) thermodynamics on a lattice

The beta function on a lattice is studied in SU(2) gluodynamics. The definition of the beta function within the scaling hypothesis at a finite lattice size is used. The functions obtained in this way are compared with the results known in the continuum limit. Graphics processing units are used as a computing platform, whereby a large amount of statistical data have been accumulated. Beta functions are analyzed for a large number of various lattices. It is shown that the beta function being studied complies with the respective analytic expression in the phase-transition region. A fast method that makes it possible to estimate the critical value of the coupling constant on a lattice is proposed.     

High temperature gluon matter in the background gauge

The polarisation tensor of gluons in high temperature QCD matter is discussed in the back-ground gauge and compared with that in the temporal axialA ₀=0 gauge. In both of these the gluon polarisation tensor alone is sufficient to give the asymptotically free sign of the QCD beta function. In the former the beta function and the imaginary part of the polarisation tensor are coupled in such a way that asymptotic freedom implies instability of plasma oscillations. In the latter, due to the non-covariance of the gauge condition, the beta function and the imaginary part are decoupled in such a way that the sign of the imaginary part corresponds to stable plasma oscillations.     

Diffractive dijet production at sqrt[s] = 630 and 1800 GeV at the Fermilab Tevatron

We report a measurement of the diffractive structure function F(D)(jj) of the antiproton obtained from a study of dijet events produced in association with a leading antiproton in pp collisions at sqrt[s] = 630 GeV at the Fermilab Tevatron. The ratio of F(D)(jj) at sqrt[s] = 630 GeV to F(D)(jj) obtained from a similar measurement at sqrt[s] = 1800 GeV is compared with expectations from QCD factorization and other theoretical predictions. We also report a measurement of the xi ( x-Pomeron) and beta ( x of parton in Pomeron) dependence of F(D)(jj) at sqrt[s] = 1800 GeV. In the region 0.035相似文献   

Optimization of angular and frequency compounding in ultrasonic attenuation estimations

Previous reports have shown that the variance in ultrasound attenuation measurements is reduced when spatial and frequency compounding were applied in data acquisition and analysis. This paper investigates factors affecting the efficiency of compound attenuation imaging methods. A theoretical expression is derived that predicts the correlation between attenuation versus frequency slope (beta) estimates as a function of the increment between measurement frequencies (deltaf ) and the angular separation between beam lines (Delta (theta)). Theoretical results are compared with those from attenuation measurements on tissue-mimicking phantoms and from simulation data. Both predictions and measurement results show that the correlation between beta estimates as a function of (Delta f ) is independent of the length of the radio frequency (rf) data segment over which beta is derived. However, it decreases with an increase in the length of the data segment used in power spectra estimates. In contrast, the correlation between beta estimates as a function of delta(theta) decreases when the rf data segment length is longer or the frequency of the signal is higher. O 2005 Acoustical Society of America.     

Energy spectrum of particles accelerated in relativistic collisionless shocks

We analytically study diffusive particle acceleration in relativistic, collisionless shocks. We find a simple relation between the spectral index s and the anisotropy of the momentum distribution along the shock front. Based on this relation, we obtain s=(3beta(u)-2beta(u)beta(2)(d)+beta(3)(d))/(beta(u)-beta(d)) for isotropic diffusion, where beta(u) (beta(d)) is the upstream (downstream) fluid velocity normalized to the speed of light. This result is in agreement with previous numerical determinations of s for all (beta(u),beta(d)), and yields s=38/9 in the ultrarelativistic limit. The spectrum-anisotropy connection is useful for testing numerical studies and constraining anisotropic diffusion results. It suggests that the spectrum is highly sensitive to the form of the diffusion function for particles traveling along the shock front.     

Renormalization group approach to the spin-1 Bose gas

A field theoretical renormalization group approach at two loop level is applied to the homogeneous spin-1 Bose gas in order to investigate the order of the phase transition. The beta function of the system with d=4-epsilon dimensions is determined up to the third power of the coupling constants and the system's free energy on the border of the classical stability is given in next to leading order. It is found that the phase transition of the interacting spin-1 Bose gases with weak spin-dependent coupling constant values is of first order.     

Laser removal of loose uranium compound contamination from metal surfaces

Pulsed laser removal of surface contamination of uranyl nitrate and uranium dioxide from stainless steel has been studied. Most of the loosely bound contamination has been removed at fluence levels below 0.5 J cm⁻², leaving about 5% fixed contamination for uranyl nitrate and 15% for uranium dioxide. Both alpha and beta activities are then sufficiently low that contaminated objects can be taken out of a restricted radiation area for re-use. The ratio of beta to alpha activity is found to be a function of particle size and changes during laser removal. In a separate experiment using technetium-99m, the collection of removed radioactivity in the filter was studied and an inventory made of removed and collected contamination.     

A GUI tool for beta function measurement using MATLAB

The beta function measurement is used to detect the shift in the betatron tune as the strength of an individual quadrupole magnet is varied. A GUI （graphic user interface） tool for the beta function measurement is developed using the MATLAB program language in the Linux environment, which facilitates the commissioning of the Shanghai Synchrotron Radiation Facility （SSRF） storage ring. In this paper, we describe the design of the application and give some measuring results and discussions about the definition of the measurement. The program has been optimized to solve some restrictions of the AT tracking code. After the correction with LOCO （linear optics from closed orbits）, the horizontal and the vertical root mean square values （rms values） can be reduced to 0.12 and 0.10.     

Dependence of the maximum energy of reflected beta-radiation on the atomic number of the reflector

The absorption method is used to establish the maximum energy for single, double, and quadruple backward scattering of beta particles as a function of the energy of the beta source and the atomic number of the target.     

Precise measurement of 14C beta spectrum by using a wall-less proportional counter

The technique and results of a precise measurement of the ¹⁴C beta spectrum in the energy range 10–160 keV by using a wall-less proportional counter are presented. The results of analysis and the inclusion of possible factors that distort the spectrum in the calculation of the detector response function are reported. Considerable deviations from the distribution expected for an allowed transition are found.     

Beta function and Schwinger functions for a many fermions system in one dimension. Anomaly of the fermi surface

We present a rigorous discussion of the analyticity properties of the beta function and of the effective potential for the theory of the ground state of a one dimensional system of many spinless fermions. We show that their analyticity domain as a function of the running couplings is a polydisk with positive radius bounded below, uniformly in, all the cut offs (infrared and ultraviolet) necessary to give a meaning to the formal Schwinger functions. We also prove the vanishing of the scale independent part of the beta function showing that this implies the analyticity of the effective potential and of the Schwinger functions in terms of the bare coupling. Finally we show that the pair Schwinger function has an anomalous long distance behaviour.