116 research outputs found
The quantum dilogarithm and representations quantum cluster varieties
We construct, using the quantum dilogarithm, a series of *-representations of
quantized cluster varieties. This includes a construction of infinite
dimensional unitary projective representations of their discrete symmetry
groups - the cluster modular groups. The examples of the latter include the
classical mapping class groups of punctured surfaces.
One of applications is quantization of higher Teichmuller spaces.
The constructed unitary representations can be viewed as analogs of the Weil
representation. In both cases representations are given by integral operators.
Their kernels in our case are the quantum dilogarithms.
We introduce the symplectic/quantum double of cluster varieties and related
them to the representations.Comment: Dedicated to David Kazhdan for his 60th birthday. The final version.
To appear in Inventiones Math. The last Section of the previous versions was
removed, and will become a separate pape
Novosibirsk hadronic currents for tau -> 4pi channels of tau decay library TAUOLA
The new parameterization of form factors developed for 4pi channels of the
tau lepton decay and based on Novosibirsk data on e^+e^- -> 4pi has been coded
in a form suitable for the TAUOLA Monte Carlo package. Comparison with results
from TAUOLA using another parameterization, i.e. the CLEO version of 1998 is
also included.Comment: 19 pages, 21 figures, LaTe
Discrete Variational Optimal Control
This paper develops numerical methods for optimal control of mechanical
systems in the Lagrangian setting. It extends the theory of discrete mechanics
to enable the solutions of optimal control problems through the discretization
of variational principles. The key point is to solve the optimal control
problem as a variational integrator of a specially constructed
higher-dimensional system. The developed framework applies to systems on
tangent bundles, Lie groups, underactuated and nonholonomic systems with
symmetries, and can approximate either smooth or discontinuous control inputs.
The resulting methods inherit the preservation properties of variational
integrators and result in numerically robust and easily implementable
algorithms. Several theoretical and a practical examples, e.g. the control of
an underwater vehicle, will illustrate the application of the proposed
approach.Comment: 30 pages, 6 figure
Discrete Nonholonomic Lagrangian Systems on Lie Groupoids
This paper studies the construction of geometric integrators for nonholonomic
systems. We derive the nonholonomic discrete Euler-Lagrange equations in a
setting which permits to deduce geometric integrators for continuous
nonholonomic systems (reduced or not). The formalism is given in terms of Lie
groupoids, specifying a discrete Lagrangian and a constraint submanifold on it.
Additionally, it is necessary to fix a vector subbundle of the Lie algebroid
associated to the Lie groupoid. We also discuss the existence of nonholonomic
evolution operators in terms of the discrete nonholonomic Legendre
transformations and in terms of adequate decompositions of the prolongation of
the Lie groupoid. The characterization of the reversibility of the evolution
operator and the discrete nonholonomic momentum equation are also considered.
Finally, we illustrate with several classical examples the wide range of
application of the theory (the discrete nonholonomic constrained particle, the
Suslov system, the Chaplygin sleigh, the Veselova system, the rolling ball on a
rotating table and the two wheeled planar mobile robot).Comment: 45 page
On scattering of solitons for the Klein-Gordon equation coupled to a particle
We establish the long time soliton asymptotics for the translation invariant
nonlinear system consisting of the Klein-Gordon equation coupled to a charged
relativistic particle. The coupled system has a six dimensional invariant
manifold of the soliton solutions. We show that in the large time approximation
any finite energy solution, with the initial state close to the solitary
manifold, is a sum of a soliton and a dispersive wave which is a solution of
the free Klein-Gordon equation. It is assumed that the charge density satisfies
the Wiener condition which is a version of the ``Fermi Golden Rule''. The proof
is based on an extension of the general strategy introduced by Soffer and
Weinstein, Buslaev and Perelman, and others: symplectic projection in Hilbert
space onto the solitary manifold, modulation equations for the parameters of
the projection, and decay of the transversal component.Comment: 47 pages, 2 figure
Radiative Scalar Meson Decays in the Light-Front Quark Model
We construct a relativistic wavefunction for scalar mesons within the
framework of light-front quark model(LFQM). This scalar wavefunction is used to
perform relativistic calculations of absolute widths for the radiative decay
processes, and
which incorporate the effects of glueball-
mixing. The mixed physical states are assumed to be ,and
for which the flavor-glue content is taken from the mixing
calculations of other works. Since experimental data for these processes are
poor, our results are compared with those of a recent non-relativistic model
calculation. We find that while the relativistic corrections introduced by the
LFQM reduce the magnitudes of the decay widths by 50-70%, the relative
strengths between different decay processes are fairly well preserved. We also
calculate decay widths for the processes and
(0^{++})\to\gamma\gamm involving the light scalars and
to test the simple model of these mesons. Our results of
model for these processes are not quite consistent with well-established data,
further supporting the idea that and are not conventional
states.Comment: 10 pages, 4 figure
Orbital stability: analysis meets geometry
We present an introduction to the orbital stability of relative equilibria of
Hamiltonian dynamical systems on (finite and infinite dimensional) Banach
spaces. A convenient formulation of the theory of Hamiltonian dynamics with
symmetry and the corresponding momentum maps is proposed that allows us to
highlight the interplay between (symplectic) geometry and (functional) analysis
in the proofs of orbital stability of relative equilibria via the so-called
energy-momentum method. The theory is illustrated with examples from finite
dimensional systems, as well as from Hamiltonian PDE's, such as solitons,
standing and plane waves for the nonlinear Schr{\"o}dinger equation, for the
wave equation, and for the Manakov system
decays and final state interactions
We study the exclusive decays of in the framework
of the perturbative QCD by identifying the as the composition of
and . We find that the
influence of the content on the predicted branching ratios is
crucial. We discuss the possible rescattering and gluonium states which could
enhance the branching ratios of considered decays. We point out that the CP
asymmetry in could be a new explorer of
.Comment: 13 pages, 2 figures, Revtex4, final version to appear in Phys. Rev.
First evidence of concurrent enzootic and endemic transmission of Ross River virus in the absence of marsupial reservoirs in Fiji
BACKGROUND:Ross River virus (RRV) is a zoonotic alphavirus transmitted by several mosquito species. Until recently, endemic transmission was only considered possible in the presence of marsupial reservoirs. METHODS:We investigated RRV seroprevalence in placental mammals, including horses, cows, goats, pigs, dogs, rats, and mice in Fiji, where there are no marsupials. A total of 302 vertebrate serum samples were collected from 86 households from 10 communities in Western Fiji. FINDINGS:Neutralizing antibodies against RRV were detected in 28 to 100% of sera depending on species, and neutralization was strong even at high dilutions. SIGNIFICANCE:Our results are unlikely to be due to cross reactions; Chikungunya is the only other alphavirus known to be present in the Pacific Islands, but it rarely spills over into non-humans, even during epidemics. Our findings, together with recent report of high RRV seroprevalence in humans, strongly suggest that RRV is circulating in Fiji in the absence of marsupial reservoirs. Considering that all non-human vertebrates present in Fiji are panglobal in distribution, RRV has the potential to further expand its geographic range. Further surveillance and access to diagnostics of RRV is critical for the early detection of emergence and outbreaks.Eri Togami, Narayan Gyawali, Oselyne Ong, Mike Kama, Van-Mai Cao-Lormeau ... Philip Weinsteini ... et al
Differential cross section and recoil polarization measurements for the gamma p to K+ Lambda reaction using CLAS at Jefferson Lab
We present measurements of the differential cross section and Lambda recoil
polarization for the gamma p to K+ Lambda reaction made using the CLAS detector
at Jefferson Lab. These measurements cover the center-of-mass energy range from
1.62 to 2.84 GeV and a wide range of center-of-mass K+ production angles.
Independent analyses were performed using the K+ p pi- and K+ p (missing pi -)
final-state topologies; results from these analyses were found to exhibit good
agreement. These differential cross section measurements show excellent
agreement with previous CLAS and LEPS results and offer increased precision and
a 300 MeV increase in energy coverage. The recoil polarization data agree well
with previous results and offer a large increase in precision and a 500 MeV
extension in energy range. The increased center-of-mass energy range that these
data represent will allow for independent study of non-resonant K+ Lambda
photoproduction mechanisms at all production angles.Comment: 22 pages, 16 figure
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