24,270 research outputs found
Global well-posedness for KdV in Sobolev Spaces of negative index
The initial value problem for the Korteweg-deVries equation on the line is
shown to be globally well-posed for rough data. In particular, we show global
well-posedness for initial data in H^s({\mathbb{R}), -3/10<s.Comment: 5 pages. Electronic Journal of Differential equations (submitted
Information on the Pion Distribution Amplitude from the Pion-Photon Transition Form Factor with the Belle and BaBar Data
The pion-photon transition form factor (TFF) provides strong constraints on
the pion distribution amplitude (DA). We perform an analysis of all existing
data (CELLO, CLEO, BaBar, Belle) on the pion-photon TFF by means of light-cone
pQCD approach in which we include the next-to-leading order correction to the
valence-quark contribution and estimate the non-valence-quark contribution by a
phenomenological model based on the TFF's limiting behavior at both
and . At present, the pion DA is not definitely determined, it is
helpful to have a pion DA model that can mimic all the suggested behaviors,
especially to agree with the constraints from the pion-photon TFF in whole
measured region within a consistent way. For the purpose, we adopt the
conventional model for pion wavefunction/DA that has been constructed in our
previous paper \cite{hw1}, whose broadness is controlled by a parameter . We
fix the DA parameters by using the CELLO, CLEO, BABAR and Belle data within the
smaller region ( GeV), where all the data are consistent
with each other. And then the pion-photon TFF is extrapolated into larger
region. We observe that the BABAR favors which has the behavior close
to the Chernyak-Zhitnitsky DA, whereas the recent Belle favors which
is close to the asymptotic DA. We need more accurate data at large region
to determine the precise value of , and the definite behavior of pion DA can
be concluded finally by the consistent data in the coming future.Comment: 6 pages, 5 figures. Slightly changed and references update
Hamiltonian Theory of Adiabatic Motion of Relativistic Charged Particles
A general Hamiltonian theory for the adiabatic motion of relativistic charged
particles confined by slowly-varying background electromagnetic fields is
presented based on a unified Lie-transform perturbation analysis in extended
phase space (which includes energy and time as independent coordinates) for all
three adiabatic invariants. First, the guiding-center equations of motion for a
relativistic particle are derived from the particle Lagrangian. Covariant
aspects of the resulting relativistic guiding-center equations of motion are
discussed and contrasted with previous works. Next, the second and third
invariants for the bounce motion and drift motion, respectively, are obtained
by successively removing the bounce phase and the drift phase from the
guiding-center Lagrangian. First-order corrections to the second and third
adiabatic invariants for a relativistic particle are derived. These results
simplify and generalize previous works to all three adiabatic motions of
relativistic magnetically-trapped particles.Comment: 20 pages, LaTeX, to appear in Physics of Plasmas (Aug, 2007
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