901 research outputs found
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
Gell-Mann - Low Function for QCD in the strong-coupling limit
The Gell-Mann - Low function \beta(g) in QCD (g=g0^2/16\pi^2 where g0 is the
coupling constant in the Lagrangian) is shown to behave in the strong-coupling
region as \beta_\infty g^\alpha with \alpha\approx -13, \beta_\infty\sim 10^5.Comment: 5 pages, PD
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
The Minimum-Uncertainty Squeezed States for for Atoms and Photons in a Cavity
We describe a six-parameter family of the minimum-uncertainty squeezed states
for the harmonic oscillator in nonrelativistic quantum mechanics. They are
derived by the action of corresponding maximal kinematical invariance group on
the standard ground state solution. We show that the product of the variances
attains the required minimum value 1/4 only at the instances that one variance
is a minimum and the other is a maximum, when the squeezing of one of the
variances occurs. The generalized coherent states are explicitly constructed
and their Wigner function is studied. The overlap coefficients between the
squeezed, or generalized harmonic, and the Fock states are explicitly evaluated
in terms of hypergeometric functions. The corresponding photons statistics are
discussed and some applications to quantum optics, cavity quantum
electrodynamics, and superfocusing in channeling scattering are mentioned.
Explicit solutions of the Heisenberg equations for radiation field operators
with squeezing are found.Comment: 27 pages, no figures, 174 references J. Phys. B: At. Mol. Opt. Phys.,
Special Issue celebrating the 20th anniversary of quantum state engineering
(R. Blatt, A. Lvovsky, and G. Milburn, Guest Editors), May 201
The Degenerate Parametric Oscillator and Ince's Equation
We construct Green's function for the quantum degenerate parametric
oscillator in terms of standard solutions of Ince's equation in a framework of
a general approach to harmonic oscillators. Exact time-dependent wave functions
and their connections with dynamical invariants and SU(1,1) group are also
discussed.Comment: 10 pages, no figure
Divergent Perturbation Series
Various perturbation series are factorially divergent. The behavior of their
high-order terms can be found by Lipatov's method, according to which they are
determined by the saddle-point configurations (instantons) of appropriate
functional integrals. When the Lipatov asymptotics is known and several lowest
order terms of the perturbation series are found by direct calculation of
diagrams, one can gain insight into the behavior of the remaining terms of the
series. Summing it, one can solve (in a certain approximation) various
strong-coupling problems. This approach is demonstrated by determining the
Gell-Mann - Low functions in \phi^4 theory, QED, and QCD for arbitrary coupling
constants. An overview of the mathematical theory of divergent series is
presented, and interpretation of perturbation series is discussed. Explicit
derivations of the Lipatov asymptotic forms are presented for some basic
problems in theoretical physics. A solution is proposed to the problem of
renormalon contributions, which hampered progress in this field in the late
1970s. Practical schemes for summation of perturbation series are described for
a coupling constant of order unity and in the strong-coupling limit. An
interpretation of the Borel integral is given for 'non-Borel-summable' series.
High-order corrections to the Lipatov asymptotics are discussed.Comment: Review article, 45 pages, PD
On the Critical Exponents for the \Lambda-Transition in Liquid Helium
The use of a new method for summing divergent series makes it possible to
significantly increase the accuracy of determining the critical exponents from
the field theoretical renormalization group. The exponent value \nu=0.6700\pm
0.0006 for the \lambda-transition in liquid helium is in good agreement with
the experiment, but contradicts the last theoretical results based on using
high-temperature series, the Monte Carlo method, and their synthesis.Comment: PDF, 7 page
Large Magnetoresistance of a Dilute -Si/SiGe/Si Quantum Well in a Parallel Magnetic Field
We report the results of an experimental study of the magnetoresistance
in two samples of -Si/SiGe/Si with low carrier concentrations
=8.2 cm and =2 cm. The
research was performed in the temperature range of 0.3-2 K in the magnetic
fields of up to 18 T, parallel to the two-dimensional (2D) channel plane at two
orientations of the in-plane magnetic field against the current
: and . In the sample
with the lowest density in the magnetic field range of 0-7.2 T the temperature
dependence of demonstrates the metallic characteristics (0). However, at =7.2 T the derivative reverses the sign. Moreover, the resistance depends on the
current orientation with respect to the in-plane magnetic field. At
13 T there is a transition from the dependence
to the dependence
. The observed effects
can be explained by the influence of the in-plane magnetic field on the orbital
motion of the charge carriers in the quasi-2D system.Comment: revised: included AC conductivity experiments to study the role of
localized state in transport; total 6 pages, 7 figures. Accepted PRB; to
appear vol.79, Issue 2
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