3,712 research outputs found
Double quantization of \cp type orbits by generalized Verma modules
It is known that symmetric orbits in for any simple Lie algebra
are equiped with a Poisson pencil generated by the
Kirillov-Kostant-Souriau bracket and the reduced Sklyanin bracket associated to
the "canonical" R-matrix. We realize quantization of this Poisson pencil on
\cp type orbits (i.e. orbits in whose real compact form is ) by means of q-deformed Verma modules.Comment: 21 pages, LaTeX, no figure
Quantum orbits of R-matrix type
Given a simple Lie algebra \gggg, we consider the orbits in \gggg^* which
are of R-matrix type, i.e., which possess a Poisson pencil generated by the
Kirillov-Kostant-Souriau bracket and the so-called R-matrix bracket. We call an
algebra quantizing the latter bracket a quantum orbit of R-matrix type. We
describe some orbits of this type explicitly and we construct a quantization of
the whole Poisson pencil on these orbits in a similar way. The notions of
q-deformed Lie brackets, braided coadjoint vector fields and tangent vector
fields are discussed as well.Comment: 18 pp., Late
Effect of Multiple Scattering on the Critical Electric Field for Runaway Electrons in the Atmosphere
A simple method for taking into account the multiple Coulomb scattering in
construction of a separatrix (the line separating the regions of runaway and
decelerating electrons in an electric field) is described. The desired line is
obtained by solving a simple transcendental equation.Comment: 3 pages, 2 figure
Remnants of dark matter clumps
What happened to the central cores of tidally destructed dark matter clumps
in the Galactic halo? We calculate the probability of surviving of the remnants
of dark matter clumps in the Galaxy by modelling the tidal destruction of the
small-scale clumps. It is demonstrated that a substantial fraction of clump
remnants may survive through the tidal destruction during the lifetime of the
Galaxy if the radius of a core is rather small. The resulting mass spectrum of
survived clumps is extended down to the mass of the core of the cosmologically
produced clumps with a minimal mass. Since the annihilation signal is dominated
by the dense part of the core, destruction of the outer part of the clump
affects the annihilation rate relatively weakly and the survived dense remnants
of tidally destructed clumps provide a large contribution to the annihilation
signal in the Galaxy. The uncertainties in minimal clump mass resulting from
the uncertainties in neutralino models are discussed.Comment: 13 pages, 6 figures, added reference
Analytic model for a frictional shallow-water undular bore
We use the integrable Kaup-Boussinesq shallow water system, modified by a
small viscous term, to model the formation of an undular bore with a steady
profile. The description is made in terms of the corresponding integrable
Whitham system, also appropriately modified by friction. This is derived in
Riemann variables using a modified finite-gap integration technique for the
AKNS scheme. The Whitham system is then reduced to a simple first-order
differential equation which is integrated numerically to obtain an asymptotic
profile of the undular bore, with the local oscillatory structure described by
the periodic solution of the unperturbed Kaup-Boussinesq system. This solution
of the Whitham equations is shown to be consistent with certain jump conditions
following directly from conservation laws for the original system. A comparison
is made with the recently studied dissipationless case for the same system,
where the undular bore is unsteady.Comment: 24 page
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