252,787 research outputs found
Chernoff's Theorem and Discrete Time Approximations of Brownian Motion on Manifolds
Let (S(t)) be a one-parameter family S = (S(t)) of positive integral
operators on a locally compact space L. For a possibly non-uniform partition of
[0,1] define a measure on the path space C([0,1],L) by using a) S(dt) for the
transition between cosecutive partition times of distance dt, and b) a suitable
continuous interpolation scheme (e.g. Brownian bridges or geodesics). If
necessary normalize to get a probability measure. We prove a version of
Chernoff's theorem of semigroup theory and tighness results which together
yield convergence in law of such measures as the partition gets finer. In
particular let L be a closed smooth submanifold of a Riemannian manifold M. We
prove convergence of Brownian motion on M, conditioned to visit L at all
partition times, to a process on L whose law has a Radon-Nikodym density with
repect to Brownian motion on L which contains scalar, mean and sectional
curvature terms. Various approximation schemes for Brownian motion are also
given. These results substantially extend earlier work by the authors and by
Andersson and Driver.Comment: 35 pages, revised version for publication, more detailed expositio
'Xenia', a new pear cultivar from Moldava, first results in the Netherlands
The pear cultivar `Xenia¿ (synonym `Noiabriskaia¿) from Moldova is a selection from a cross between `Triomphe de Vienne¿ and `Nicolai Krier¿. In The Netherlands, `Xenia¿ has been tested since 2001. So far, trees have given early and high yields and required little thinning. Up to now, a very low to moderate susceptibility to scab (Venturia pirinia) and a very low susceptibility to fruit tree canker (Nectria galligena) have been observed. The trees showed a medium vigour and there was a low tendency to biennial bearing. With the relatively young trees, the average fruit size of `Xenia¿ fruits at full crop was 250-300 g. The harvest window was wide. Fruits of `Xenia¿ had a green ground colour at harvest and were moderately bronzed. `Xenia¿ had a spherical pear shape. The fruits had a strong fruit skin. The firmness was higher than that of `Conference¿. The juiciness varied from juicy to very juicy, depending on the maturity stage. `Xenia¿ had a good eating quality: fresh, slightly aromatic with a typical aroma. The storability of the fruits was very good and the shelf life of `Xenia¿ proved to be much better than of `Conference¿. Summarizing, the first results show a good potential for commercial fruit growing
Observability of an induced electric dipole moment of the neutron from nonlinear QED
It has been shown recently that a neutron placed in an external quasistatic
electric field develops an induced electric dipole moment
due to quantum fluctuations in the QED vacuum. A
feasible experiment which could detect such an effect is proposed and described
here. It is shown that the peculiar angular dependence of
on the orientation of the neutron spin leads to a
characteristic asymmetry in polarized neutron scattering by heavy nuclei. This
asymmetry can be of the order of for neutrons with epithermal
energies. For thermalized neutrons from a hot moderator one still expects
experimentally accessible values of the order of . The contribution of
the induced effect to the neutron scattering length is expected to be only one
order of magnitude smaller than that due to the neutron polarizability from its
quark substructure. The experimental observation of this scattering asymmetry
would be the first ever signal of nonlinearity in electrodynamics due to
quantum fluctuations in the QED vacuum
The Landau-Lifshitz-Bloch equation for ferrimagnetic materials
We derive the Landau-Lifshitz-Bloch (LLB) equation for a two-component
magnetic system valid up to the Curie temperature. As an example, we consider
disordered GdFeCo ferrimagnet where the ultrafast optically induced
magnetization switching under the action of heat alone has been recently
reported. The two-component LLB equation contains the longitudinal relaxation
terms responding to the exchange fields from the proper and the neighboring
sublattices. We show that the sign of the longitudinal relaxation rate at high
temperatures can change depending on the dynamical magnetization value and a
dynamical polarisation of one material by another can occur. We discuss the
differences between the LLB and the Baryakhtar equation, recently used to
explain the ultrafast switching in ferrimagnets. The two-component LLB equation
forms basis for the largescale micromagnetic modeling of nanostructures at high
temperatures and ultrashort timescales
Energies of Quantum QED Flux Tubes
In this talk I present recent studies on vacuum polarization energies and
energy densities induced by QED flux tubes. I focus on comparing three and four
dimensional scenarios and the discussion of various approximation schemes in
view of the exact treatment.Comment: 9 pages latex, Talk presented at the QFEXT 05 workshop in Barcelona,
Sept. 2005. To appear in the proceeding
Asymmetric quantum dot in microcavity as a nonlinear optical element
We have investigated theoretically the interaction between individual quantum
dot with broken inversion symmetry and electromagnetic field of a single-mode
quantum microcavity. It is shown that in the strong coupling regime the system
demonstrates nonlinear optical properties and can serve as emitter of the
terahertz radiation at Rabi frequency of the system. Analytical results for
simplest physical situations are obtained and numerical quantum approach for
calculating emission spectrum is developed.Comment: Article is accepted to Phys. Rev. A (7 pages, 5 figures
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