4,278 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
The Trajectory-Coherent Approximation and the System of Moments for the Hartree-Type Equation
The general construction of quasi-classically concentrated solutions to the
Hartree-type equation, based on the complex WKB-Maslov method, is presented.
The formal solutions of the Cauchy problem for this equation, asymptotic in
small parameter \h (\h\to0), are constructed with a power accuracy of
O(\h^{N/2}), where N is any natural number. In constructing the
quasi-classically concentrated solutions, a set of Hamilton-Ehrenfest equations
(equations for middle or centered moments) is essentially used. The nonlinear
superposition principle has been formulated for the class of quasi-classically
concentrated solutions of the Hartree-type equations. The results obtained are
exemplified by the one-dimensional equation Hartree-type with a Gaussian
potential.Comments: 6 pages, 4 figures, LaTeX Report no: Subj-class:
Accelerator PhysicsComment: 36 pages, LaTeX-2
The evolution operator of the Hartree-type equation with a quadratic potential
Based on the ideology of the Maslov's complex germ theory, a method has been
developed for finding an exact solution of the Cauchy problem for a
Hartree-type equation with a quadratic potential in the class of
semiclassically concentrated functions. The nonlinear evolution operator has
been obtained in explicit form in the class of semiclassically concentrated
functions. Parametric families of symmetry operators have been found for the
Hartree-type equation. With the help of symmetry operators, families of exact
solutions of the equation have been constructed. Exact expressions are obtained
for the quasi-energies and their respective states. The Aharonov-Anandan
geometric phases are found in explicit form for the quasi-energy states.Comment: 23 pege
The relation of global magnetic solar field indices and solar wind characteristics with long-term variations of galactic cosmic rays
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