1,443 research outputs found
Hadronic Light-by-Light Scattering in the Muonium Hyperfine Splitting
We consider an impact of hadronic light-by-light scattering on the muonium
hyperfine structure. A shift of the hyperfine interval is calculated with the light-by-light scattering approximated
by exchange of pseudoscalar and pseudovector mesons. Constraints from the
operator product expansion in QCD are used to fix parameters of the model
similar to the one used earlier for the hadronic light-by-light scattering in
calculations of the muon anomalous magnetic moment. The pseudovector exchange
is dominant in the resulting shift, . Although the effect is tiny it is useful in understanding
the level of hadronic uncertainties.Comment: 16 pages, 7 figures, a reference adde
Wave propagation through a coherently amplifying random medium
We report a detailed and systematic numerical study of wave propagation
through a coherently amplifying random one-dimensional medium. The coherent
amplification is modeled by introducing a uniform imaginary part in the site
energies of the disordered single-band tight binding Hamiltonian. Several
distinct length scales (regimes), most of them new, are identified from the
behavior of transmittance and reflectance as a function of the material
parameters. We show that the transmittance is a non-self-averaging quantity
with a well defined mean value. The stationary distribution of the super
reflection differs qualitatively from the analytical results obtained within
the random phase approximation in strong disorder and amplification regime. The
study of the stationary distribution of the phase of the reflected wave reveals
the reason for this discrepancy. The applicability of random phase
approximation is discussed. We emphasize the dual role played by the lasing
medium, as an amplifier as well as a reflector.Comment: 33 pages RevTex, 14 EPS figures included, Accepted for publication in
IJMP-
Melnikov theory to all orders and Puiseux series for subharmonic solutions
We study the problem of subharmonic bifurcations for analytic systems in the
plane with perturbations depending periodically on time, in the case in which
we only assume that the subharmonic Melnikov function has at least one zero. If
the order of zero is odd, then there is always at least one subharmonic
solution, whereas if the order is even in general other conditions have to be
assumed to guarantee the existence of subharmonic solutions. Even when such
solutions exist, in general they are not analytic in the perturbation
parameter. We show that they are analytic in a fractional power of the
perturbation parameter. To obtain a fully constructive algorithm which allows
us not only to prove existence but also to obtain bounds on the radius of
analyticity and to approximate the solutions within any fixed accuracy, we need
further assumptions. The method we use to construct the solution -- when this
is possible -- is based on a combination of the Newton-Puiseux algorithm and
the tree formalism. This leads to a graphical representation of the solution in
terms of diagrams. Finally, if the subharmonic Melnikov function is identically
zero, we show that it is possible to introduce higher order generalisations,
for which the same kind of analysis can be carried out.Comment: 30 pages, 6 figure
On cogrowth function of algebras and its logarithmical gap
Let be an associative algebra. A finite word
over alphabet is {\it-reducible} if its image in is a -linear
combination of length-lexicographically lesser words. An {\it obstruction} in a
subword-minimal -reducible word. A {\em cogrowth} function is number of
obstructions of length . We show that the cogrowth function of a
finitely presented algebra is either bounded or at least logarithmical. We also
show that an uniformly recurrent word has at least logarithmical cogrowth.Comment: 5 page
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