65,123 research outputs found
The tensor structure on the representation category of the triplet algebra
We study the braided monoidal structure that the fusion product induces on
the abelian category -mod, the category of representations of
the triplet -algebra . The -algebras are a
family of vertex operator algebras that form the simplest known examples of
symmetry algebras of logarithmic conformal field theories. We formalise the
methods for computing fusion products, developed by Nahm, Gaberdiel and Kausch,
that are widely used in the physics literature and illustrate a systematic
approach to calculating fusion products in non-semi-simple representation
categories. We apply these methods to the braided monoidal structure of
-mod, previously constructed by Huang, Lepowsky and Zhang, to
prove that this braided monoidal structure is rigid. The rigidity of
-mod allows us to prove explicit formulae for the fusion product
on the set of all simple and all projective -modules, which were
first conjectured by Fuchs, Hwang, Semikhatov and Tipunin; and Gaberdiel and
Runkel.Comment: 58 pages; edit: added references and revisions according to referee
reports. Version to appear on J. Phys.
Markov quantum fields on a manifold
We study scalar quantum field theory on a compact manifold. The free theory
is defined in terms of functional integrals. For positive mass it is shown to
have the Markov property in the sense of Nelson. This property is used to
establish a reflection positivity result when the manifold has a reflection
symmetry. In dimension d=2 we use the Markov property to establish a sewing
operation for manifolds with boundary circles. Also in d=2 the Markov property
is proved for interacting fields.Comment: 14 pages, 1 figure, Late
Full Hydrodynamic Model of Nonlinear Electromagnetic Response in Metallic Metamaterials
Applications of metallic metamaterials have generated significant interest in
recent years. Electromagnetic behavior of metamaterials in the optical range is
usually characterized by a local-linear response. In this article, we develop a
finite-difference time-domain (FDTD) solution of the hydrodynamic model that
describes a free electron gas in metals. Extending beyond the local-linear
response, the hydrodynamic model enables numerical investigation of nonlocal
and nonlinear interactions between electromagnetic waves and metallic
metamaterials. By explicitly imposing the current continuity constraint, the
proposed model is solved in a self-consistent manner. Charge, energy and
angular momentum conservation laws of high-order harmonic generation have been
demonstrated for the first time by the Maxwell-hydrodynamic FDTD model. The
model yields nonlinear optical responses for complex metallic metamaterials
irradiated by a variety of waveforms. Consequently, the multiphysics model
opens up unique opportunities for characterizing and designing nonlinear
nanodevices.Comment: 11 pages, 14 figure
An energetic blast wave from the December 27 giant flare of the soft gamma-ray repeater 1806-20
Recent follow-up observations of the December 27 giant flare of SGR 1806-20
have detected a multiple-frequency radio afterglow from 240 MHz to 8.46 GHz,
extending in time from a week to about a month after the flare. The angular
size of the source was also measured for the first time. Here we show that this
radio afterglow gives the first piece of clear evidence that an energetic blast
wave sweeps up its surrounding medium and produces a synchrotron afterglow, the
same mechanism as established for gamma-ray burst afterglows. The optical
afterglow is expected to be intrinsically as bright as at t\la
0.1 days after the flare, but very heavy extinction makes the detection
difficult because of the low galactic latitude of the source. Rapid infrared
follow-up observations to giant flares are therefore crucial for the
low-latitude SGRs, while for high-latitude SGRs (e.g. SGR 0526-66), rapid
follow-ups should result in identification of their possible optical
afterglows. Rapid multi-wavelength follow-ups will also provide more detailed
information of the early evolution of a fireball as well as its composition.Comment: Updated version, accepted for publication in ApJ Letter
A Two-Component Explosion Model for the Giant Flare and Radio Afterglow from SGR1806-20
The brightest giant flare from the soft -ray repeater (SGR) 1806-20
was detected on 2004 December 27. The isotropic-equivalent energy release of
this burst is at least one order of magnitude more energetic than those of the
two other SGR giant flares. Starting from about one week after the burst, a
very bright ( mJy), fading radio afterglow was detected. Follow-up
observations revealed the multi-frequency light curves of the afterglow and the
temporal evolution of the source size. Here we show that these observations can
be understood in a two-component explosion model. In this model, one component
is a relativistic collimated outflow responsible for the initial giant flare
and the early afterglow, and another component is a subrelativistic wider
outflow responsible for the late afterglow. We also discuss triggering
mechanisms of these two components within the framework of the magnetar model.Comment: 7 pages including 3 figures, emulateapj5.sty, accepted for
publication in ApJ Letter
Nuclear Chemical and Mechanical Instability and the Liquid-Gas Phase Transition in Nuclei
The thermodynamic properties of nuclei are studied in a mean field model
using a Skryme interaction. Properties of two component systems are
investigated over the complete range of proton fraction from a system of pure
neutrons to a system of only protons. Besides volume, symmetry, and Coulomb
effects we also include momentum or velocity dependent forces. Applications of
the results developed are then given which include nuclear mechanical and
chemical instability and an associated liquid/gas phase transition in two
component systems. The velocity dependence leads to further changes in the
coexistence curve and nuclear mechanical and chemical instability curves.Comment: 21 pages, 9 figures, Results are changed due to error in progra
Transition amplitudes and sewing properties for bosons on the Riemann sphere
We consider scalar quantum fields on the sphere, both massive and massless.
In the massive case we show that the correlation functions define amplitudes
which are trace class operators between tensor products of a fixed Hilbert
space. We also establish certain sewing properties between these operators. In
the massless case we consider exponential fields and have a conformal field
theory. In this case the amplitudes are only bilinear forms but still we
establish sewing properties. Our results are obtained in a functional integral
framework.Comment: 33 page
On Gravitational anomaly and Hawking radiation near weakly isolated horizon
Based on the idea of the work by Wilczek and his collaborators, we consider
the gravitational anomaly near weekly isolated horizon. We find that there
exists a universal choice of tortoise coordinate for any weakly isolated
horizon. Under this coordinate, the leading behavior of a quite arbitrary
scalar field near horizon is a 2-dimensional chiral scalar field. This means we
can extend the idea of Wilczek and his collaborators to more general cases and
show the relation between gravitational anomaly and Hawking radiation is a
universal property of black hole horizon.Comment: 14 page
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