1,180 research outputs found
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
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
Renormalons and Analytic Properties of the \beta function
The presence or absense of renormalon singularities in the Borel plane is
shown to be determined by the analytic properties of the Gell-Mann - Low
function \beta(g) and some other functions. A constructive criterion for the
absense of singularities consists in the proper behavior of the \beta function
and its Borel image B(z) at infinity, \beta(g)\sim g^\alpha and B(z)\sim
z^\alpha with \alpha\le 1. This criterion is probably fulfilled for the \phi^4
theory, QED and QCD, but is violated in the O(n)-symmetric sigma model with
n\to\infty.Comment: 6 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
H-theorem in quantum physics
Remarkable progress of quantum information theory (QIT) allowed to formulate
mathematical theorems for conditions that data-transmitting or data-processing
occurs with a non-negative entropy gain. However, relation of these results
formulated in terms of entropy gain in quantum channels to temporal evolution
of real physical systems is not thoroughly understood. Here we build on the
mathematical formalism provided by QIT to formulate the quantum H-theorem in
terms of physical observables. We discuss the manifestation of the second law
of thermodynamics in quantum physics and uncover special situations where the
second law can be violated. We further demonstrate that the typical evolution
of energy-isolated quantum systems occurs with non-diminishing entropy.Comment: 8 pages, 4 figure
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
Triviality problem and the high-temperature expansions of the higher susceptibilities for the Ising and the scalar field models on four-, five- and six-dimensional lattices
High-temperature expansions are presently the only viable approach to the
numerical calculation of the higher susceptibilities for the spin and the
scalar-field models on high-dimensional lattices. The critical amplitudes of
these quantities enter into a sequence of universal amplitude-ratios which
determine the critical equation of state. We have obtained a substantial
extension through order 24, of the high-temperature expansions of the free
energy (in presence of a magnetic field) for the Ising models with spin s >=
1/2 and for the lattice scalar field theory with quartic self-interaction, on
the simple-cubic and the body-centered-cubic lattices in four, five and six
spatial dimensions. A numerical analysis of the higher susceptibilities
obtained from these expansions, yields results consistent with the widely
accepted ideas, based on the renormalization group and the constructive
approach to Euclidean quantum field theory, concerning the no-interaction
("triviality") property of the continuum (scaling) limit of spin-s Ising and
lattice scalar-field models at and above the upper critical dimensionality.Comment: 17 pages, 10 figure
Enumeration of many-body skeleton diagrams
The many-body dynamics of interacting electrons in condensed matter and
quantum chemistry is often studied at the quasiparticle level, where the
perturbative diagrammatic series is partially resummed. Based on Hedin's
equations for self-energy, polarization, propagator, effective potential, and
vertex function in zero dimension of space-time, dressed Feynman (skeleton)
diagrams are enumerated. Such diagram counts provide useful basic checks for
extensions of the theory for future realistic simulations.Comment: 5 pages including 4 figure
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