52,763 research outputs found
Gravitational waves from black hole collisions via an eclectic approach
We present the first results in a new program intended to make the best use
of all available technologies to provide an effective understanding of waves
from inspiralling black hole binaries in time for imminent observations. In
particular, we address the problem of combining the close-limit approximation
describing ringing black holes and full numerical relativity, required for
essentially nonlinear interactions. We demonstrate the effectiveness of our
approach using general methods for a model problem, the head-on collision of
black holes. Our method allows a more direct physical understanding of these
collisions indicating clearly when non-linear methods are important. The
success of this method supports our expectation that this unified approach will
be able to provide astrophysically relevant results for black hole binaries in
time to assist gravitational wave observations.Comment: 4 pages, 3 eps figures, Revte
Confinement: Understanding the Relation Between the Wilson Loop and Dual Theories of Long Distance Yang Mills Theory
In this paper we express the velocity dependent, spin dependent heavy quark
potential in QCD in terms of a Wilson Loop determined
by pure Yang Mills theory. We use an effective dual theory of long-distance
Yang Mills theory to calculate for large loops; i.e. for loops of
size . ( is the flux tube radius, fixed by the value of the
Higgs (monopole) mass of the dual theory, which is a concrete realization of
the Mandelstam 't Hooft dual superconductor mechanism of confinement).
We replace by , given by a functional integral
over the dual variables, which for can be evaluated by a
semiclassical expansion, since the dual theory is weakly coupled at these
distances. The classical approximation gives the leading contribution to
and yields a velocity dependent heavy quark potential which
for large becomes linear in , and which for small approaches lowest
order perturbative QCD. This latter fact means that these results should remain
applicable down to distances where radiative corrections giving rise to a
running coupling constant become important. The spin dependence of the
potential reflects the vector coupling of the quarks at long range as well as
at short range. The methods developed here should be applicable to any
realization of the dual superconductor mechanism. They give an expression
determining independent of the classical approximation, but
semi classical corrections due to fluctuations of the flux tube are not worked
out in this paper. Taking these into account should lead to an effective string
theory free from the conformal anomaly.Comment: 39 pages, latex2e, 1 figure(fig.eps
Nonlinear Integral-Equation Formulation of Orthogonal Polynomials
The nonlinear integral equation P(x)=\int_alpha^beta dy w(y) P(y) P(x+y) is
investigated. It is shown that for a given function w(x) the equation admits an
infinite set of polynomial solutions P(x). For polynomial solutions, this
nonlinear integral equation reduces to a finite set of coupled linear algebraic
equations for the coefficients of the polynomials. Interestingly, the set of
polynomial solutions is orthogonal with respect to the measure x w(x). The
nonlinear integral equation can be used to specify all orthogonal polynomials
in a simple and compact way. This integral equation provides a natural vehicle
for extending the theory of orthogonal polynomials into the complex domain.
Generalizations of the integral equation are discussed.Comment: 7 pages, result generalized to include integration in the complex
domai
Incorporating spatial correlations into multispecies mean-field models
In biology, we frequently observe different species existing within the same environment. For example, there are many cell types in a tumour, or different animal species may occupy a given habitat. In modeling interactions between such species, we often make use of the mean-field approximation, whereby spatial correlations between the locations of individuals are neglected. Whilst this approximation holds in certain situations, this is not always the case, and care must be taken to ensure the mean-field approximation is only used in appropriate settings. In circumstances where the mean-field approximation is unsuitable, we need to include information on the spatial distributions of individuals, which is not a simple task. In this paper, we provide a method that overcomes many of the failures of the mean-field approximation for an on-lattice volume-excluding birth-death-movement process with multiple species. We explicitly take into account spatial information on the distribution of individuals by including partial differential equation descriptions of lattice site occupancy correlations. We demonstrate how to derive these equations for the multispecies case and show results specific to a two-species problem. We compare averaged discrete results to both the mean-field approximation and our improved method, which incorporates spatial correlations. We note that the mean-field approximation fails dramatically in some cases, predicting very different behavior from that seen upon averaging multiple realizations of the discrete system. In contrast, our improved method provides excellent agreement with the averaged discrete behavior in all cases, thus providing a more reliable modeling framework. Furthermore, our method is tractable as the resulting partial differential equations can be solved efficiently using standard numerical techniques
Effective String Theory of Vortices and Regge Trajectories
Starting from a field theory containing classical vortex solutions, we obtain
an effective string theory of these vortices as a path integral over the two
transverse degrees of freedom of the string. We carry out a semiclassical
expansion of this effective theory, and use it to obtain corrections to Regge
trajectories due to string fluctuations.Comment: 27 pages, revtex, 3 figures, corrected an error with the cutoff in
appendix E (was previously D), added more discussion of Fig. 3, moved some
material in section 9 to a new appendi
On the evaluation formula for Jack polynomials with prescribed symmetry
The Jack polynomials with prescribed symmetry are obtained from the
nonsymmetric polynomials via the operations of symmetrization,
antisymmetrization and normalization. After dividing out the corresponding
antisymmetric polynomial of smallest degree, a symmetric polynomial results. Of
interest in applications is the value of the latter polynomial when all the
variables are set equal. Dunkl has obtained this evaluation, making use of a
certain skew symmetric operator. We introduce a simpler operator for this
purpose, thereby obtaining a new derivation of the evaluation formula. An
expansion formula of a certain product in terms of Jack polynomials with
prescribed symmetry implied by the evaluation formula is used to derive a
generalization of a constant term identity due to Macdonald, Kadell and Kaneko.
Although we don't give the details in this work, the operator introduced here
can be defined for any reduced crystallographic root system, and used to
provide an evaluation formula for the corresponding Heckman-Opdam polynomials
with prescribed symmetry.Comment: 18 page
Pade Improvement of the Free Energy in High Temperature QCD
Pade approximants (PA's) are constructed from the perturbative coefficients
of the free energy through O(g^5) in hot QCD. Pade summation is shown to reduce
the renormalization-scale dependence substantially even at temperature (T) as
low as 250 MeV.
Also, PA's predict that the free energy does not deviate more than 10 % from
the Stefan-Boltzmann limit for T > 250 MeV.Comment: Typos corrected. Minor changes in the text and references. To appear
in Phys. Rev.
Thermodynamics of localized magnetic moments in a Dirac conductor
We show that the magnetic susceptibility of a dilute ensemble of magnetic
impurities in a conductor with a relativistic electronic spectrum is
non-analytic in the inverse tempertature at . We derive a general
theory of this effect and construct the high-temperature expansion for the
disorder averaged susceptibility to any order, convergent at all tempertaures
down to a possible ordering transition. When applied to Ising impurities on a
surface of a topological insulator, the proposed general theory agrees with
Monte Carlo simulations, and it allows us to find the critical temperature of
the ferromagnetic phase transition.Comment: 5 pages, 1 figure, 2 tables, RevTe
Renormalization Group Functions for Two-Dimensional Phase Transitions: To the Problem of Singular Contributions
According to the available publications, the field theoretical
renormalization group (RG) approach in the two-dimensional case gives the
critical exponents that differ from the known exact values. This fact was
attempted to explain by the existence of nonanalytic contributions in the RG
functions. The situation is analysed in this work using a new algorithm for
summing divergent series that makes it possible to analyse dependence of the
results for the critical exponents on the expansion coefficients for RG
functions. It has been shown that the exact values of all the exponents can be
obtained with a reasonable form of the coefficient functions. These functions
have small nonmonotonities or inflections, which are poorly reproduced in
natural interpolations. It is not necessary to assume the existence of singular
contributions in RG functions.Comment: PDF, 11 page
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