3,142 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
Efficiency of using East Kazakhstan natural sorbents in water purification from ions of heavy metals (Cu2+)
Sorption properties of bentonite clays of East Kazakhstan have been studied by the example of model solutions containing ions of copper (Cu2+). The mechanism of exchange and degree of ion extraction from solutions were establishe
Efficiency of using East Kazakhstan natural sorbents in water purification from ions of heavy metals (Cu2+)
Sorption properties of bentonite clays of East Kazakhstan have been studied by the example of model solutions containing ions of copper (Cu2+). The mechanism of exchange and degree of ion extraction from solutions were establishe
Switching from visibility to invisibility via Fano resonances: theory and experiment
Subwavelength structures demonstrate many unusual optical properties which
can be employed for engineering functional metadevices, as well as scattering
of light and invisibility cloaking. Here we demonstrate that the suppression of
light scattering for any direction of observation can be achieved for an
uniform dielectric object with high refractive index, in a sharp contrast to
the cloaking with multilayered plasmonic structures suggested previously. Our
finding is based on the novel physics of cascades of Fano resonances observed
in the Mie scattering from a homogeneous dielectric rod. We observe this effect
experimentally at microwaves by employing high temperature-dependent dielectric
permittivity of a glass cylinder with heated water. Our results open a new
avenue in analyzing the optical response of hight-index dielectric
nanoparticles and the physics of cloaking.Comment: 8 pages, 4 figure
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