1,244 research outputs found
Renormalization : A number theoretical model
We analyse the Dirichlet convolution ring of arithmetic number theoretic
functions. It turns out to fail to be a Hopf algebra on the diagonal, due to
the lack of complete multiplicativity of the product and coproduct. A related
Hopf algebra can be established, which however overcounts the diagonal. We
argue that the mechanism of renormalization in quantum field theory is modelled
after the same principle. Singularities hence arise as a (now continuously
indexed) overcounting on the diagonals. Renormalization is given by the map
from the auxiliary Hopf algebra to the weaker multiplicative structure, called
Hopf gebra, rescaling the diagonals.Comment: 15 pages, extended version of talks delivered at SLC55 Bertinoro,Sep
2005, and the Bob Delbourgo QFT Fest in Hobart, Dec 200
On the statistics of resonances and non-orthogonal eigenfunctions in a model for single-channel chaotic scattering
We describe analytical and numerical results on the statistical properties of
complex eigenvalues and the corresponding non-orthogonal eigenvectors for
non-Hermitian random matrices modeling one-channel quantum-chaotic scattering
in systems with broken time-reversal invariance.Comment: 4 pages, 2 figure
On the Floquet Theory of Delay Differential Equations
We present an analytical approach to deal with nonlinear delay differential
equations close to instabilities of time periodic reference states. To this end
we start with approximately determining such reference states by extending the
Poincar'e Lindstedt and the Shohat expansions which were originally developed
for ordinary differential equations. Then we systematically elaborate a linear
stability analysis around a time periodic reference state. This allows to
approximately calculate the Floquet eigenvalues and their corresponding
eigensolutions by using matrix valued continued fractions
Fabrication of low-loss SOI nano-waveguides including BEOL processes for nonlinear applications
We report successful fabrication of low-loss SOI nano-waveguides with integrated PIN diode structures. The entire fabrication process is done on a 200 mm BiCMOS toolset using front-end-of-line (FEOL) and back-end-of-line (BEOL) processes and does not show any undesirable influence upon the photonic performance. Such a waveguide technology forms an attractive platform for a wide range of nonlinear applications due to efficient free carrier removal as well as use of standard substrates and processing technology. Nonlinear experiments were conducted to investigate the potential of the introduced technology. The performance of the designed waveguides can be used as a benchmark for future development of proposed platform for integrated silicon photonics and electronics circuits
Comparison of the bifurcation scenarios predicted by the single-mode and multimode semiconductor laser rate equations
We present a detailed comparison of the bifurcation scenarios predicted by single-mode and multimode semiconductor laser rate equation models under large amplitude injection current modulation. The influence of the gain model on the predicted dynamics is investigated. Calculations of the dependence of the time averaged longitudinal mode intensities on modulation frequency are compared with experiments performed on an AlxGa1-xAs Fabry-Pérot semiconductor laser.K. A. Corbett and M. W. Hamilto
Hadronic Loop Corrections to the Muon Anomalous Magnetic Moment
The dominant theoretical uncertainties in both, the anomalous magnetic moment
of the muon and the value of the electromagnetic coupling at the Z scale arise
from their hadronic contributions. Since these will ultimately dominate the
experimental errors, we study the correlation between them, as well as with
other fundamental parameters. To this end we present analytical formulas for
the QCD contribution from higher energies and from heavy quarks. Including
these correlations affects the Higgs boson mass extracted from precision data.Comment: 4 page
Testing new physics with the electron g-2
We argue that the anomalous magnetic moment of the electron (a_e) can be used
to probe new physics. We show that the present bound on new-physics
contributions to a_e is 8*10^-13, but the sensitivity can be improved by about
an order of magnitude with new measurements of a_e and more refined
determinations of alpha in atomic-physics experiments. Tests on new-physics
effects in a_e can play a crucial role in the interpretation of the observed
discrepancy in the anomalous magnetic moment of the muon (a_mu). In a large
class of models, new contributions to magnetic moments scale with the square of
lepton masses and thus the anomaly in a_mu suggests a new-physics effect in a_e
of (0.7 +- 0.2)*10^-13. We also present examples of new-physics theories in
which this scaling is violated and larger effects in a_e are expected. In such
models the value of a_e is correlated with specific predictions for processes
with violation of lepton number or lepton universality, and with the electric
dipole moment of the electron.Comment: 34 pages, 7 figures. Minor changes and references adde
MicroRNA-221 and -222 modulate intestinal inflammatory Th17 cell response as negative feedback regulators downstream of interleukin-23
Mikami et al. examine the role of miR-221/222 in helper T cells in the gut. MiR-221/222 are induced by IL-23 and suppressed by TGFβ, targeting Maf and IL23r for degradation. During inflammation, these miRNAs serve as a negative feedback rheostat to constrain IL23-Th17 cell responses
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