68,471 research outputs found
A non-variational approach to nonlinear stability in stellar dynamics applied to the King model
In previous work by Y. Guo and G. Rein, nonlinear stability of equilibria in
stellar dynamics, i.e., of steady states of the Vlasov-Poisson system, was
accessed by variational techniques. Here we propose a different,
non-variational technique and use it to prove nonlinear stability of the King
model against a class of spherically symmetric, dynamically accessible
perturbations. This model is very important in astrophysics and was out of
reach of the previous techniques
Constructions of free commutative integro-differential algebras
In this survey, we outline two recent constructions of free commutative
integro-differential algebras. They are based on the construction of free
commutative Rota-Baxter algebras by mixable shuffles. The first is by
evaluations. The second is by the method of Gr\"obner-Shirshov bases.Comment: arXiv admin note: substantial text overlap with arXiv:1302.004
Plasmon assisted transmission of high dimensional orbital angular momentum entangled state
We present an experimental evidence that high dimensional orbital angular
momentum entanglement of a pair of photons can be survived after a
photon-plasmon-photon conversion. The information of spatial modes can be
coherently transmitted by surface plasmons. This experiment primarily studies
the high dimensional entangled systems based on surface plasmon with
subwavelength structures. It maybe useful in the investigation of spatial mode
properties of surface plasmon assisted transmission through subwavelength hole
arrays.Comment: 7 pages,6 figure
Free Rota-Baxter algebras and rooted trees
A Rota-Baxter algebra, also known as a Baxter algebra, is an algebra with a
linear operator satisfying a relation, called the Rota-Baxter relation, that
generalizes the integration by parts formula. Most of the studies on
Rota-Baxter algebras have been for commutative algebras. Two constructions of
free commutative Rota-Baxter algebras were obtained by Rota and Cartier in the
1970s and a third one by Keigher and one of the authors in the 1990s in terms
of mixable shuffles. Recently, noncommutative Rota-Baxter algebras have
appeared both in physics in connection with the work of Connes and Kreimer on
renormalization in perturbative quantum field theory, and in mathematics
related to the work of Loday and Ronco on dendriform dialgebras and
trialgebras.
This paper uses rooted trees and forests to give explicit constructions of
free noncommutative Rota--Baxter algebras on modules and sets. This highlights
the combinatorial nature of Rota--Baxter algebras and facilitates their further
study. As an application, we obtain the unitarization of Rota-Baxter algebras.Comment: 23 page
Spitzer's Identity and the Algebraic Birkhoff Decomposition in pQFT
In this article we continue to explore the notion of Rota-Baxter algebras in
the context of the Hopf algebraic approach to renormalization theory in
perturbative quantum field theory. We show in very simple algebraic terms that
the solutions of the recursively defined formulae for the Birkhoff
factorization of regularized Hopf algebra characters, i.e. Feynman rules,
naturally give a non-commutative generalization of the well-known Spitzer's
identity. The underlying abstract algebraic structure is analyzed in terms of
complete filtered Rota-Baxter algebras.Comment: 19 pages, 2 figure
Interactions of Charmed Mesons with Light Pseudoscalar Mesons from Lattice QCD and Implications on the Nature of the D_{s0}^*(2317)
We study the scattering of light pseudoscalar mesons (, ) off charmed
mesons (, ) in full lattice QCD. The S-wave scattering lengths are
calculated using L\"uscher's finite volume technique. We use a relativistic
formulation for the charm quark. For the light quark, we use domain-wall
fermions in the valence sector and improved Kogut-Susskind sea quarks. We
calculate the scattering lengths of isospin-3/2 , , ,
isospin-0 and isospin-1 channels on the lattice. For the
chiral extrapolation, we use a chiral unitary approach to next-to-leading
order, which at the same time allows us to give predictions for other channels.
It turns out that our results support the interpretation of the
as a molecule. At the same time, we also update a
prediction for the isospin breaking hadronic decay width
to keV.Comment: 22 pages, 5 figures; a typo in Table II corrected (for the
coefficients of the NLO amplitudes
Magnetic anisotropy and spin-spiral wave in V, Cr and Mn atomic chains on Cu(001) surface: First principles calculations
Recent ab intio studies of the magnetic properties of all 3d transition
metal(TM) freestanding atomic chains predicted that these nanowires could have
a giant magnetic anisotropy energy (MAE) and might support a spin-spiral
structure, thereby suggesting that these nanowires would have technological
applicationsin, e.g., high density magnetic data storages. In order to
investigate how the substrates may affect the magnetic properties of the
nanowires, here we systematically study the V, Cr and Mn linear atomic chains
on the Cu(001) surface based on the density functional theory with the
generalized gradient approximation. We find that V, Cr, and Mn linear chains on
the Cu(001) surface still have a stable or metastable ferromagnetic state.
However, the ferromagnetic state is unstable against formation of a
noncollinear spin-spiral structure in the Mn linear chains and also the V
linear chain on the atop sites on the Cu(001) surface, due to the frustrated
magnetic interactions in these systems. Nonetheless, the presence of the
Cu(001) substrate does destabilize the spin-spiral state already present in the
freestanding V linear chain and stabilizes the ferromagnetic state in the V
linear chain on the hollow sites on Cu(001). When spin-orbit coupling (SOC) is
included, the spin magnetic moments remain almost unchanged, due to the
weakness of SOC in 3d TM chains. Furthermore, both the orbital magnetic moments
and MAEs for the V, Cr and Mn are small, in comparison with both the
corresponding freestanding nanowires and also the Fe, Co and Ni linear chains
on the Cu (001) surface.Comment: Accepted for publication in J. Phys. D: Applied Physic
Generation of N-qubit W state with rf-SQUID qubits by adiabatic passage
A simple scheme is presented to generate n-qubit W state with
rf-superconducting quantum interference devices (rf-SQUIDs) in cavity QED
through adiabatic passage. Because of the achievable strong coupling for
rf-SQUID qubits embedded in cavity QED, we can get the desired state with high
success probability. Furthermore, the scheme is insensitive to position
inaccuracy of the rf-SQUIDs. The numerical simulation shows that, by using
present experimental techniques, we can achieve our scheme with very high
success probability, and the fidelity could be eventually unity with the help
of dissipation.Comment: to appear in Phys. Rev.
Mixable Shuffles, Quasi-shuffles and Hopf Algebras
The quasi-shuffle product and mixable shuffle product are both
generalizations of the shuffle product and have both been studied quite
extensively recently. We relate these two generalizations and realize
quasi-shuffle product algebras as subalgebras of mixable shuffle product
algebras. As an application, we obtain Hopf algebra structures in free
Rota-Baxter algebras.Comment: 14 pages, no figure, references update
Snyder's Quantized Space-time and De Sitter Special Relativity
There is a one-to-one correspondence between Snyder's model in de Sitter
space of momenta and the \dS-invariant special relativity. This indicates that
physics at the Planck length and the scale should be
dual to each other and there is in-between gravity of local \dS-invariance
characterized by a dimensionless coupling constant .Comment: 8 page
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