2,193 research outputs found
Nonlinear dynamics of soft fermion excitations in hot QCD plasma III: Soft-quark bremsstrahlung and energy losses
In general line with our early works [Yu.A. Markov, M.A. Markova, Nucl. Phys.
A770 (2006) 162; 784 (2007) 443] within the framework of a semiclassical
approximation the general theory of calculation of effective currents and
sources generating bremsstrahlung of an arbitrary number of soft quarks and
soft gluons at collision of a high-energy color-charged particle with thermal
partons in a hot quark-gluon plasma, is developed. For the case of one- and
two-scattering thermal partons with radiation of one or two soft excitations,
the effective currents and sources are calculated in an explicit form. In the
model case of `frozen' medium, approximate expressions for energy losses
induced by the most simple processes of bremsstrahlung of soft quark and soft
gluon, are derived. On the basis of a conception of the mutual cancellation of
singularities in the sum of so-called `diagonal' and `off-diagonal'
contributions to the energy losses, an effective method of determining color
factors in scattering probabilities, containing the initial values of Grassmann
color charges, is suggested. The dynamical equations for Grassmann color
charges of hard particle used by us early are proved to be insufficient for
investigation of the higher radiative processes. It is shown that for correct
description of these processes the given equations should be supplemented
successively with the higher-order terms in powers of the soft fermionic field.Comment: 93 pages, 20 figure
Subexponential estimations in Shirshov's height theorem (in English)
In 1993 E. I. Zelmanov asked the following question in Dniester Notebook:
"Suppose that F_{2, m} is a 2-generated associative ring with the identity
x^m=0. Is it true, that the nilpotency degree of F_{2, m} has exponential
growth?" We show that the nilpotency degree of l-generated associative algebra
with the identity x^d=0 is smaller than Psi(d,d,l), where Psi(n,d,l)=2^{18} l
(nd)^{3 log_3 (nd)+13}d^2. We give the definitive answer to E. I. Zelmanov by
this result. It is the consequence of one fact, which is based on combinatorics
of words. Let l, n and d>n be positive integers. Then all the words over
alphabet of cardinality l which length is greater than Psi(n,d,l) are either
n-divided or contain d-th power of subword, where a word W is n-divided, if it
can be represented in the following form W=W_0 W_1...W_n such that W_1 >'
W_2>'...>'W_n. The symbol >' means lexicographical order here. A. I. Shirshov
proved that the set of non n-divided words over alphabet of cardinality l has
bounded height h over the set Y consisting of all the words of degree <n.
Original Shirshov's estimation was just recursive, in 1982 double exponent was
obtained by A.G.Kolotov and in 1993 A.Ya.Belov obtained exponential estimation.
We show, that h<Phi(n,l), where Phi(n,l) = 2^{87} n^{12 log_3 n + 48} l. Our
proof uses Latyshev idea of Dilworth theorem application.Comment: 21 pages, Russian version of the article is located at the link
arXiv:1101.4909; Sbornik: Mathematics, 203:4 (2012), 534 -- 55
Solar activity beyond the disk and variations of the cosmic ray gradient
Part of galactic cosmic rays (CR) observed near the Earth and on the Earth come from beyond-disk regions of circumsolar space. But CR of those energies which undergo substantial modulation cover too large a path across the lines of force of the interplanetary magnetic field (IMF) in order that they could provide an effective transfer of information about beyond-disk solar activity. And if it is still possible, the most probable channel for transferring such information must be a neutral layer of heliomagnetosphere in which the transverse CR transport is facilitated by their drift in an inhomogeneous magnetic field. A simple diffusion model for an expected CR variation in a neutral layer near the Earth is discussed. It is of importance that variations of the CR gradient are not at all always accompanied by considerable variations of IMF and solar wind velocity at the point of observation
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