379 research outputs found
Symplectically degenerate maxima via generating functions
We provide a simple proof of a theorem due to Nancy Hingston, asserting that
symplectically degenerate maxima of any Hamiltonian diffeomorphism of the
standard symplectic 2d-torus are non-isolated contractible periodic points or
their action is a non-isolated point of the average-action spectrum. Our
argument is based on generating functions.Comment: 25 pages, thoroughly revised version, new titl
The Conley Conjecture and Beyond
This is (mainly) a survey of recent results on the problem of the existence
of infinitely many periodic orbits for Hamiltonian diffeomorphisms and Reeb
flows. We focus on the Conley conjecture, proved for a broad class of closed
symplectic manifolds, asserting that under some natural conditions on the
manifold every Hamiltonian diffeomorphism has infinitely many (simple) periodic
orbits. We discuss in detail the established cases of the conjecture and
related results including an analog of the conjecture for Reeb flows, the cases
where the conjecture is known to fail, the question of the generic existence of
infinitely many periodic orbits, and local geometrical conditions that force
the existence of infinitely many periodic orbits. We also show how a recently
established variant of the Conley conjecture for Reeb flows can be applied to
prove the existence of infinitely many periodic orbits of a low-energy charge
in a non-vanishing magnetic field on a surface other than a sphere.Comment: 34 pages, 1 figur
AKSZ construction from reduction data
We discuss a general procedure to encode the reduction of the target space
geometry into AKSZ sigma models. This is done by considering the AKSZ
construction with target the BFV model for constrained graded symplectic
manifolds. We investigate the relation between this sigma model and the one
with the reduced structure. We also discuss several examples in dimension two
and three when the symmetries come from Lie group actions and systematically
recover models already proposed in the literature.Comment: 42 page
Emergent Gauge Fields in Holographic Superconductors
Holographic superconductors have been studied so far in the absence of
dynamical electromagnetic fields, namely in the limit in which they coincide
with holographic superfluids. It is possible, however, to introduce dynamical
gauge fields if a Neumann-type boundary condition is imposed on the
AdS-boundary. In 3+1 dimensions, the dual theory is a 2+1 dimensional CFT whose
spectrum contains a massless gauge field, signaling the emergence of a gauge
symmetry. We study the impact of a dynamical gauge field in vortex
configurations where it is known to significantly affect the energetics and
phase transitions. We calculate the critical magnetic fields H_c1 and H_c2,
obtaining that holographic superconductors are of Type II (H_c1 < H_c2). We
extend the study to 4+1 dimensions where the gauge field does not appear as an
emergent phenomena, but can be introduced, by a proper renormalization, as an
external dynamical field. We also compare our predictions with those arising
from a Ginzburg-Landau theory and identify the generic properties of Abrikosov
vortices in holographic models.Comment: 19 pages, 14 figures, few comments added, version published in JHE
Modular classes of skew algebroid relations
Skew algebroid is a natural generalization of the concept of Lie algebroid.
In this paper, for a skew algebroid E, its modular class mod(E) is defined in
the classical as well as in the supergeometric formulation. It is proved that
there is a homogeneous nowhere-vanishing 1-density on E* which is invariant
with respect to all Hamiltonian vector fields if and only if E is modular, i.e.
mod(E)=0. Further, relative modular class of a subalgebroid is introduced and
studied together with its application to holonomy, as well as modular class of
a skew algebroid relation. These notions provide, in particular, a unified
approach to the concepts of a modular class of a Lie algebroid morphism and
that of a Poisson map.Comment: 20 page
Some Recent Developments on Kink Collisions and Related Topics
We review recent works on modeling of dynamics of kinks in 1+1 dimensional
theory and other related models, like sine-Gordon model or
theory. We discuss how the spectral structure of small perturbations can affect
the dynamics of non-perturbative states, such as kinks or oscillons. We
describe different mechanisms, which may lead to the occurrence of the resonant
structure in the kink-antikink collisions. We explain the origin of the
radiation pressure mechanism, in particular, the appearance of the negative
radiation pressure in the and models. We also show that the
process of production of the kink-antikink pairs, induced by radiation is
chaotic.Comment: 26 pages, 9 figures; invited chapter to "A dynamical perspective on
the {\phi}4 model: Past, present and future", Eds. P.G. Kevrekidis and J.
Cuevas-Maraver; Springer book class with svmult.cls include
Controlling Cherenkov angles with resonance transition radiation
Cherenkov radiation provides a valuable way to identify high energy particles
in a wide momentum range, through the relation between the particle velocity
and the Cherenkov angle. However, since the Cherenkov angle depends only on
material's permittivity, the material unavoidably sets a fundamental limit to
the momentum coverage and sensitivity of Cherenkov detectors. For example, Ring
Imaging Cherenkov detectors must employ materials transparent to the frequency
of interest as well as possessing permittivities close to unity to identify
particles in the multi GeV range, and thus are often limited to large gas
chambers. It would be extremely important albeit challenging to lift this
fundamental limit and control Cherenkov angles as preferred. Here we propose a
new mechanism that uses constructive interference of resonance transition
radiation from photonic crystals to generate both forward and backward
Cherenkov radiation. This mechanism can control Cherenkov angles in a flexible
way with high sensitivity to any desired range of velocities. Photonic crystals
thus overcome the severe material limit for Cherenkov detectors, enabling the
use of transparent materials with arbitrary values of permittivity, and provide
a promising option suited for identification of particles at high energy with
enhanced sensitivity.Comment: There are 16 pages and 4 figures for the manuscript. Supplementary
information with 18 pages and 5 figures, appended at the end of the file with
the manuscript. Source files in Word format converted to PDF. Submitted to
Nature Physic
Cosmic ray diffusion near the Bohm limit in the Cassiopeia A supernova remnant
Supernova remnants (SNRs) are believed to be the primary location of the
acceleration of Galactic cosmic rays, via diffusive shock (Fermi) acceleration.
Despite considerable theoretical work the precise details are still unknown, in
part because of the difficulty in directly observing nucleons that are
accelerated to TeV energies in, and affect the structure of, the SNR shocks.
However, for the last ten years, X-ray observatories ASCA, and more recently
Chandra, XMM-Newton, and Suzaku have made it possible to image the synchrotron
emission at keV energies produced by cosmic-ray electrons accelerated in the
SNR shocks. In this article, we describe a spatially-resolved spectroscopic
analysis of Chandra observations of the Galactic SNR Cassiopeia A to map the
cutoff frequencies of electrons accelerated in the forward shock. We set upper
limits on the electron diffusion coefficient and find locations where particles
appear to be accelerated nearly as fast as theoretically possible (the Bohm
limit).Comment: 18 pages, 5 figures. Accepted for publication in Nature Physics (DOI
below), final version available week of August 28, 2006 at
http://www.nature.com/nphy
Young neutron stars with soft gamma ray emission and anomalous X-ray pulsar
The observational properties of Soft Gamma Repeaters and Ano\-malous X-ray
Pulsars (SGR/AXP) indicate to necessity of the energy source different from a
rotational energy of a neutron star. The model, where the source of the energy
is connected with a magnetic field dissipation in a highly magnetized neutron
star (magnetar) is analyzed. Some observational inconsistencies are indicated
for this interpretation. The alternative energy source, connected with the
nuclear energy of superheavy nuclei stored in the nonequilibrium layer of low
mass neutron star is discussed.Comment: 29 pages, 13 figures, Springer International Publishing Switzerland
2016 A.W. Alsabti, P. Murdin (eds.), Handbook of Supernova
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