8,570 research outputs found
Loop Corrections in the Spectrum of 2D Hawking Radiation
We determine the one-loop and the two-loop back-reaction corrections in the
spectrum of the Hawking radiation for the CGHS model of 2d dilaton gravity by
evaluating the Bogoliubov coefficients for a massless scalar field propagating
on the corresponding backgrounds. Since the back-reaction can induce a small
shift in the position of the classical horizon, we find that a positive shift
leads to a non-Planckian late-time spectrum, while a null or a negative shift
leads to a Planckian late-time spectrum in the leading-order stationary-point
approximation. In the one-loop case there are no corrections to the classical
Hawking temperature, while in the two-loop case the temperature is three times
greater than the classical value. We argue that these results are consistent
with the behaviour of the Hawking flux obtained from the operator quantization
only for the times which are not too late, in accordance with the limits of
validity of the semiclassical approximation.Comment: 20 pages, latex, no figure
Enteral Nutrition and Acute Pancreatitis: A Review
Introduction. In patients with acute pancreatitis (AP), nutritional support is required if normal food cannot be tolerated within several days. Enteral nutrition is preferred over parenteral nutrition. We reviewed the literature about enteral nutrition in AP. Methods. A MEDLINE search of the English language literature between 1999–2009. Results. Nasogastric tube feeding appears to be safe and well tolerated in the majority of patients with severe AP, rendering the concept of pancreatic rest less probable. Enteral nutrition has a beneficial influence on the outcome of AP and should probably be initiated as early as possible (within 48 hours). Supplementation of enteral formulas with glutamine or prebiotics and probiotics cannot routinely be recommended. Conclusions. Nutrition therapy in patients with AP emerged from supportive adjunctive therapy to a proactive primary intervention. Large multicentre studies are needed to confirm the safety and effectiveness of nasogastric feeding and to investigate the role of early nutrition support
Future asymptotic expansions of Bianchi VIII vacuum metrics
Bianchi VIII vacuum solutions to Einstein's equations are causally
geodesically complete to the future, given an appropriate time orientation, and
the objective of this article is to analyze the asymptotic behaviour of
solutions in this time direction. For the Bianchi class A spacetimes, there is
a formulation of the field equations that was presented in an article by
Wainwright and Hsu, and in a previous article we analyzed the asymptotic
behaviour of solutions in these variables. One objective of this paper is to
give an asymptotic expansion for the metric. Furthermore, we relate this
expansion to the topology of the compactified spatial hypersurfaces of
homogeneity. The compactified spatial hypersurfaces have the topology of
Seifert fibred spaces and we prove that in the case of NUT Bianchi VIII
spacetimes, the length of a circle fibre converges to a positive constant but
that in the case of general Bianchi VIII solutions, the length tends to
infinity at a rate we determine.Comment: 50 pages, no figures. Erronous definition of Seifert fibred spaces
correcte
The Non-Trapping Degree of Scattering
We consider classical potential scattering. If no orbit is trapped at energy
E, the Hamiltonian dynamics defines an integer-valued topological degree. This
can be calculated explicitly and be used for symbolic dynamics of
multi-obstacle scattering.
If the potential is bounded, then in the non-trapping case the boundary of
Hill's Region is empty or homeomorphic to a sphere.
We consider classical potential scattering. If at energy E no orbit is
trapped, the Hamiltonian dynamics defines an integer-valued topological degree
deg(E) < 2. This is calculated explicitly for all potentials, and exactly the
integers < 2 are shown to occur for suitable potentials.
The non-trapping condition is restrictive in the sense that for a bounded
potential it is shown to imply that the boundary of Hill's Region in
configuration space is either empty or homeomorphic to a sphere.
However, in many situations one can decompose a potential into a sum of
non-trapping potentials with non-trivial degree and embed symbolic dynamics of
multi-obstacle scattering. This comprises a large number of earlier results,
obtained by different authors on multi-obstacle scattering.Comment: 25 pages, 1 figure Revised and enlarged version, containing more
detailed proofs and remark
Direct instantons, topological charge screening and QCD glueball sum rules
Nonperturbative Wilson coefficients of the operator product expansion (OPE)
for the spin-0 glueball correlators are derived and analyzed. A systematic
treatment of the direct instanton contributions is given, based on realistic
instanton size distributions and renormalization at the operator scale. In the
pseudoscalar channel, topological charge screening is identified as an
additional source of (semi-) hard nonperturbative physics. The screening
contributions are shown to be vital for consistency with the anomalous axial
Ward identity, and previously encountered pathologies (positivity violations
and the disappearance of the 0^{-+} glueball signal) are traced to their
neglect. On the basis of the extended OPE, a comprehensive quantitative
analysis of eight Borel-moment sum rules in both spin-0 glueball channels is
then performed. The nonperturbative OPE coefficients turn out to be
indispensable for consistent sum rules and for their reconciliation with the
underlying low-energy theorems. The topological short-distance physics strongly
affects the sum rule results and reveals a rather diverse pattern of glueball
properties. New predictions for the spin-0 glueball masses and decay constants
and an estimate of the scalar glueball width are given, and several
implications for glueball structure and experimental glueball searches are
discussed.Comment: 49 pages, 8 figure
The Quantum Mellin transform
We uncover a new type of unitary operation for quantum mechanics on the
half-line which yields a transformation to ``Hyperbolic phase space''. We show
that this new unitary change of basis from the position x on the half line to
the Hyperbolic momentum , transforms the wavefunction via a Mellin
transform on to the critial line . We utilise this new transform
to find quantum wavefunctions whose Hyperbolic momentum representation
approximate a class of higher transcendental functions, and in particular,
approximate the Riemann Zeta function. We finally give possible physical
realisations to perform an indirect measurement of the Hyperbolic momentum of a
quantum system on the half-line.Comment: 23 pages, 6 Figure
Perturbed Three Vortex Dynamics
It is well known that the dynamics of three point vortices moving in an ideal
fluid in the plane can be expressed in Hamiltonian form, where the resulting
equations of motion are completely integrable in the sense of Liouville and
Arnold. The focus of this investigation is on the persistence of regular
behavior (especially periodic motion) associated to completely integrable
systems for certain (admissible) kinds of Hamiltonian perturbations of the
three vortex system in a plane. After a brief survey of the dynamics of the
integrable planar three vortex system, it is shown that the admissible class of
perturbed systems is broad enough to include three vortices in a half-plane,
three coaxial slender vortex rings in three-space, and `restricted' four vortex
dynamics in a plane. Included are two basic categories of results for
admissible perturbations: (i) general theorems for the persistence of invariant
tori and periodic orbits using Kolmogorov-Arnold-Moser and Poincare-Birkhoff
type arguments; and (ii) more specific and quantitative conclusions of a
classical perturbation theory nature guaranteeing the existence of periodic
orbits of the perturbed system close to cycles of the unperturbed system, which
occur in abundance near centers. In addition, several numerical simulations are
provided to illustrate the validity of the theorems as well as indicating their
limitations as manifested by transitions to chaotic dynamics.Comment: 26 pages, 9 figures, submitted to the Journal of Mathematical Physic
Hodge Theory on Metric Spaces
Hodge theory is a beautiful synthesis of geometry, topology, and analysis,
which has been developed in the setting of Riemannian manifolds. On the other
hand, spaces of images, which are important in the mathematical foundations of
vision and pattern recognition, do not fit this framework. This motivates us to
develop a version of Hodge theory on metric spaces with a probability measure.
We believe that this constitutes a step towards understanding the geometry of
vision.
The appendix by Anthony Baker provides a separable, compact metric space with
infinite dimensional \alpha-scale homology.Comment: appendix by Anthony W. Baker, 48 pages, AMS-LaTeX. v2: final version,
to appear in Foundations of Computational Mathematics. Minor changes and
addition
Topological complexity of the relative closure of a semi-Pfaffian couple
Gabrielov introduced the notion of relative closure of a Pfaffian couple as
an alternative construction of the o-minimal structure generated by
Khovanskii's Pfaffian functions. In this paper, use the notion of format (or
complexity) of a Pfaffian couple to derive explicit upper-bounds for the
homology of its relative closure.
Keywords: Pfaffian functions, fewnomials, o-minimal structures, Betti
numbers.Comment: 12 pages, 1 figure. v3: Proofs and bounds have been slightly improve
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