665 research outputs found
Singular solutions to the Seiberg-Witten and Freund equations on flat space from an iterative method
Although it is well known that the Seiberg-Witten equations do not admit
nontrivial solutions in flat space, singular solutions to them have been
previously exhibited -- either in or in the dimensionally reduced spaces
and -- which have physical interest. In this work, we employ an
extension of the Hopf fibration to obtain an iterative procedure to generate
particular singular solutions to the Seiberg-Witten and Freund equations on
flat space. Examples of solutions obtained by such method are presented and
briefly discussed.Comment: 7 pages, minor changes. To appear in J. Math. Phy
Binary Black Hole Mergers from Planet-like Migrations
If supermassive black holes (BHs) are generically present in galaxy centers,
and if galaxies are built up through hierarchical merging, BH binaries are at
least temporary features of most galactic bulges. Observations suggest,
however, that binary BHs are rare, pointing towards a binary lifetime far
shorter than the Hubble time. We show that, regardless of the detailed
mechanism, all stellar-dynamical processes are insufficient to reduce
significantly the orbital separation once orbital velocities in the binary
exceed the virial velocity of the system. We propose that a massive gas disk
surrounding a BH binary can effect its merger rapidly, in a scenario analogous
to the orbital decay of super-jovian planets due to a proto-planetary disk. As
in the case of planets, gas accretion onto the secondary (here a supermassive
BH) is integrally connected with its inward migration. Such accretion would
give rise to quasar activity. BH binary mergers could therefore be responsible
for many or most quasars.Comment: 8 pages, submitted to ApJ Letter
Liouville Vortex And Kink Solutions Of The Seiberg--Witten Equations
The Seiberg--Witten equations, when dimensionally reduced to \bf R^{2}\mit,
naturally yield the Liouville equation, whose solutions are parametrized by an
arbitrary analytic function . The magnetic flux is the integral of
a singular Kaehler form involving ; for an appropriate choice of ,
coaxial or separated vortex configurations with are
obtained when the integral is regularized. The regularized connection in the
\bf R^{1}\mit case coincides with the kink solution of theory.Comment: 14 pages, Late
Fractional Dirac Bracket and Quantization for Constrained Systems
So far, it is not well known how to deal with dissipative systems. There are
many paths of investigation in the literature and none of them present a
systematic and general procedure to tackle the problem. On the other hand, it
is well known that the fractional formalism is a powerful alternative when
treating dissipative problems. In this paper we propose a detailed way of
attacking the issue using fractional calculus to construct an extension of the
Dirac brackets in order to carry out the quantization of nonconservative
theories through the standard canonical way. We believe that using the extended
Dirac bracket definition it will be possible to analyze more deeply gauge
theories starting with second-class systems.Comment: Revtex 4.1. 9 pages, two-column. Final version to appear in Physical
Review
Coadjoint orbits of the Virasoro algebra and the global Liouville equation
The classification of the coadjoint orbits of the Virasoro algebra is
reviewed and is then applied to analyze the so-called global Liouville
equation. The review is self-contained, elementary and is tailor-made for the
application. It is well-known that the Liouville equation for a smooth, real
field under periodic boundary condition is a reduction of the SL(2,R)
WZNW model on the cylinder, where the WZNW field g in SL(2,R) is restricted to
be Gauss decomposable. If one drops this restriction, the Hamiltonian reduction
yields, for the field where is a constant,
what we call the global Liouville equation. Corresponding to the winding number
of the SL(2,R) WZNW model there is a topological invariant in the reduced
theory, given by the number of zeros of Q over a period. By the substitution
, the Liouville theory for a smooth is recovered in
the trivial topological sector. The nontrivial topological sectors can be
viewed as singular sectors of the Liouville theory that contain blowing-up
solutions in terms of . Since the global Liouville equation is
conformally invariant, its solutions can be described by explicitly listing
those solutions for which the stress-energy tensor belongs to a set of
representatives of the Virasoro coadjoint orbits chosen by convention. This
direct method permits to study the `coadjoint orbit content' of the topological
sectors as well as the behaviour of the energy in the sectors. The analysis
confirms that the trivial topological sector contains special orbits with
hyperbolic monodromy and shows that the energy is bounded from below in this
sector only.Comment: Plain TEX, 48 pages, final version to appear in IJMP
Representations of an integer by some quaternary and octonary quadratic forms
In this paper we consider certain quaternary quadratic forms and octonary
quadratic forms and by using the theory of modular forms, we find formulae for
the number of representations of a positive integer by these quadratic forms.Comment: 20 pages, 4 tables. arXiv admin note: text overlap with
arXiv:1607.0380
Onsager-Manning-Oosawa condensation phenomenon and the effect of salt
Making use of results pertaining to Painleve III type equations, we revisit
the celebrated Onsager-Manning-Oosawa condensation phenomenon for charged stiff
linear polymers, in the mean-field approximation with salt. We obtain
analytically the associated critical line charge density, and show that it is
severely affected by finite salt effects, whereas previous results focused on
the no salt limit. In addition, we obtain explicit expressions for the
condensate thickness and the electric potential. The case of asymmetric
electrolytes is also briefly addressed.Comment: to appear in Phys. Rev. Let
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