1,622 research outputs found
Magnetic moment of an electron near a surface with dispersion
Boundary-dependent radiative corrections that modify the magnetic moment of an electron near a dielectric or conducting surface are investigated. Normal-mode quantization of the electromagnetic field and perturbation theory applied to the Dirac equation for a charged particle in a weak magnetic field yield a general formula for the magnetic moment correction in terms of any choice of electromagnetic mode functions. For two particular models, a non-dispersive dielectric and an undamped plasma, it is shown that, by using contour integration techniques over a complex wave vector, this can be simplified to a formula featuring just integrals over TE and TM reflection coefficients of the surface. Analysing the magnetic moment correction for several models of surfaces, we obtain markedly different results from the previously considered simplistic 'perfect reflector' model, which is due to the inclusion of physically important features of the surface like evanescent field modes and dispersion in the material. Remarkably, for a general dispersive dielectric surface, the magnetic moment correction of an electron nearby has a peak whose position and height can be tuned by choice of material parameters
Quantum electrodynamics of a free particle near dispersive dielectric or conducting boundaries
Quantum electrodynamics near a boundary is investigated by considering the
inertial mass shift of an electron near a dielectric or conducting surface. We
show that in all tractable cases the shift can be written in terms of integrals
over the TE and TM reflection coefficients associated with the surface, in
analogy to the Lifshitz formula for the Casimir effect. We discuss the
applications and potential limitations of this formula, and provide exact
results for several models of the surface
Analysis of Fourier transform valuation formulas and applications
The aim of this article is to provide a systematic analysis of the conditions
such that Fourier transform valuation formulas are valid in a general
framework; i.e. when the option has an arbitrary payoff function and depends on
the path of the asset price process. An interplay between the conditions on the
payoff function and the process arises naturally. We also extend these results
to the multi-dimensional case, and discuss the calculation of Greeks by Fourier
transform methods. As an application, we price options on the minimum of two
assets in L\'evy and stochastic volatility models.Comment: 26 pages, 3 figures, to appear in Appl. Math. Financ
3-manifolds with(out) metrics of nonpositive curvature
In the context of Thurstons geometrisation program we address the question
which compact aspherical 3-manifolds admit Riemannian metrics of nonpositive
curvature. We show that non-geometric Haken manifolds generically, but not
always, admit such metrics. More precisely, we prove that a Haken manifold
with, possibly empty, boundary of zero Euler characteristic admits metrics of
nonpositive curvature if the boundary is non-empty or if at least one atoroidal
component occurs in its canonical topological decomposition. Our arguments are
based on Thurstons Hyperbolisation Theorem. We give examples of closed
graph-manifolds with linear gluing graph and arbitrarily many Seifert
components which do not admit metrics of nonpositive curvature.Comment: 16 page
Anomalous magnetic moment of an electron near a dispersive surface
Changes in the magnetic moment of an electron near a dielectric or conducting surface due to boundary-dependent radiative corrections are investigated. The electromagnetic field is quantized by normal mode expansion for a nondispersive dielectric and an undamped plasma, but the electron is described by the Dirac equation without matter-field quantization. Perturbation theory in the Dirac equation leads to a general formula for the magnetic-moment shift in terms of integrals over products of electromagnetic mode functions. In each of the models investigated, contour integration techniques over a complex wave vector can be used to derive a general formula featuring just integrals over transverse electric and transverse magnetic reflection coefficients of the surface. Analysis of the magnetic-moment shift for several classes of materials yields markedly different results from the previously considered simplistic “perfect-reflector” model, due to the inclusion of physically important features of the electromagnetic response of the surface such as evanescent field modes and dispersion in the material. For a general dispersive dielectric surface, the magnetic-moment shift of a nearby electron can exceed the previous prediction of the perfect-reflector model by several orders of magnitude
Sonoluminescence as a QED vacuum effect. II: Finite Volume Effects
In a companion paper [quant-ph/9904013] we have investigated several
variations of Schwinger's proposed mechanism for sonoluminescence. We
demonstrated that any realistic version of Schwinger's mechanism must depend on
extremely rapid (femtosecond) changes in refractive index, and discussed ways
in which this might be physically plausible. To keep that discussion tractable,
the technical computations in that paper were limited to the case of a
homogeneous dielectric medium. In this paper we investigate the additional
complications introduced by finite-volume effects. The basic physical scenario
remains the same, but we now deal with finite spherical bubbles, and so must
decompose the electromagnetic field into Spherical Harmonics and Bessel
functions. We demonstrate how to set up the formalism for calculating Bogolubov
coefficients in the sudden approximation, and show that we qualitatively retain
the results previously obtained using the homogeneous-dielectric (infinite
volume) approximation.Comment: 23 pages, LaTeX 209, ReV-TeX 3.2, five figure
Quantum Electrodynamics near a Dielectric Half-space
We determine the photon propagator in the presence of a non-dispersive
dielectric half-space and use it to calculate the self-energy of an electron
near a dielectric surface
Gauge Theories with Cayley-Klein and Gauge Groups
Gauge theories with the orthogonal Cayley-Klein gauge groups and
are regarded. For nilpotent values of the contraction
parameters these groups are isomorphic to the non-semisimple Euclid,
Newton, Galilei groups and corresponding matter spaces are fiber spaces with
degenerate metrics. It is shown that the contracted gauge field theories
describe the same set of fields and particle mass as gauge
theories, if Lagrangians in the base and in the fibers all are taken into
account. Such theories based on non-semisimple contracted group provide more
simple field interactions as compared with the initial ones.Comment: 14 pages, 5 figure
3D printed fracture reduction guides planned and printed at the point of care show high accuracy - a porcine feasibility study.
PURPOSE
After surgical treatment of comminuted diaphyseal femoral and tibial fractures, relevant malalignment, especially rotational errors occur in up to 40-50%. This either results in a poor clinical outcome or requires revision surgery. This study aims to evaluate the accuracy of reduction if surgery is supported by 3D guides planned and printed at the point of care.
METHODS
Ten porcine legs underwent computed tomography (CT) and 3D models of femur and tibia were built. Reduction guides were virtually constructed and fitted to the proximal and distal metaphysis. The guides were 3D printed using medically approved resin. Femoral and tibial comminuted diaphyseal fractures were simulated and subsequently reduced using the 3D guides. Postoperative 3D bone models were reconstructed to compare the accuracy to the preoperative planning.
RESULTS
Femoral reduction showed a mean deviation ± SD from the plan of 1.0 mm ± 0.9 mm for length, 0.9° ± 0.7° for varus/valgus, 1.2° ± 0.9° for procurvatum/recurvatum and 2.0° ± 1.7° for rotation. Analysis of the tibial reduction revealed a mean deviation ± SD of 2.4 mm ± 1.6 mm for length, 1.0° ± 0.6° for varus/valgus, 1.3° ± 1.4° for procurvatum/recurvatum and 2.9° ± 2.2° for rotation.
CONCLUSIONS
This study shows high accuracy of reduction with 3D guides planned and printed at the point of care. Applied to a clinical setting, this technique has the potential to avoid malreduction and consecutive revision surgery in comminuted diaphyseal fractures.
LEVEL OF EVIDENCE
Basic Science
Vortex in a trapped Bose-Einstein condensate with dipole-dipole interactions
We calculate the critical rotation frequency at which a vortex state becomes
energetically favorable over the vortex-free ground state in a harmonically
trapped Bose-Einstein condensate whose atoms have dipole-dipole interactions as
well as the usual s-wave contact interactions. In the Thomas-Fermi
(hydrodynamic) regime, dipolar condensates in oblate cylindrical traps (with
the dipoles aligned along the axis of symmetry of the trap) tend to have lower
critical rotation frequencies than their purely s-wave contact interaction
counterparts. The converse is true for dipolar condensates in prolate traps.
Quadrupole excitations and centre of mass motion are also briefly discussed as
possible competing mechanisms to a vortex as means by which superfluids with
partially attractive interactions might carry angular momentumComment: 12 pages, 12 figure
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