628 research outputs found
Resonance-Induced Effects in Photonic Crystals
For the case of a simple face-centered-cubic photonic crystal of homogeneous
dielectric spheres, we examine to what extent single-sphere Mie resonance
frequencies are related to band gaps and whether the width of a gap can be
enlarged due to nearby resonances. Contrary to some suggestions, no spectacular
effects may be expected. When the dielectric constant of the spheres
is greater than the dielectric constant of the
background medium, then for any filling fraction there exists a critical
above which the lowest lying Mie resonance frequency falls inside
the lowest stop gap in the (111) crystal direction, close to its midgap
frequency. If , the correspondence between Mie
resonances and both the (111) stop gap and a full gap does not follow such a
regular pattern. If the Mie resonance frequency is close to a gap edge, one can
observe a resonance-induced widening of a relative gap width by .Comment: 14 pages, 3 figs., RevTex. For more info look at
http://www.amolf.nl/external/wwwlab/atoms/theory/index.htm
A simple formula for the L-gap width of a face-centered-cubic photonic crystal
The width of the first Bragg's scattering peak in the (111)
direction of a face-centered-cubic lattice of air spheres can be well
approximated by a simple formula which only involves the volume averaged
and over the lattice unit cell, being the
(position dependent) dielectric constant of the medium, and the effective
dielectric constant in the long-wavelength limit approximated
by Maxwell-Garnett's formula. Apparently, our formula describes the asymptotic
behaviour of the absolute gap width for high dielectric contrast
exactly. The standard deviation steadily decreases well below
1% as increases. For example for the sphere filling
fraction and . On the interval , our
formula still approximates the absolute gap width (the relative
gap width ) with a reasonable precision, namely with a standard
deviation 3% (4.2%) for low filling fractions up to 6.5% (8%) for the
close-packed case. Differences between the case of air spheres in a dielectric
and dielectric spheres in air are briefly discussed.Comment: 13 pages, 4 figs., RevTex, two references added. For more info see
http://www.amolf.nl/external/wwwlab/atoms/theory/index.htm
How many orthonormal bases are needed to distinguish all pure quantum states?
We collect some recent results that together provide an almost complete
answer to the question stated in the title. For the dimension d=2 the answer is
three. For the dimensions d=3 and d>4 the answer is four. For the dimension d=4
the answer is either three or four. Curiously, the exact number in d=4 seems to
be an open problem
Photonic Band Gaps of Three-Dimensional Face-Centered Cubic Lattices
We show that the photonic analogue of the Korringa-Kohn-Rostocker method is a
viable alternative to the plane-wave method to analyze the spectrum of
electromagnetic waves in a three-dimensional periodic dielectric lattice.
Firstly, in the case of an fcc lattice of homogeneous dielectric spheres, we
reproduce the main features of the spectrum obtained by the plane wave method,
namely that for a sufficiently high dielectric contrast a full gap opens in the
spectrum between the eights and ninth bands if the dielectric constant
of spheres is lower than the dielectric constant of
the background medium. If , no gap is found in the
spectrum. The maximal value of the relative band-gap width approaches 14% in
the close-packed case and decreases monotonically as the filling fraction
decreases. The lowest dielectric contrast for which a
full gap opens in the spectrum is determined to be 8.13. Eventually, in the
case of an fcc lattice of coated spheres, we demonstrate that a suitable
coating can enhance gap widths by as much as 50%.Comment: 19 pages, 6 figs., plain latex - a section on coated spheres, two
figures, and a few references adde
Pauli problem for a spin of arbitrary length: A simple method to determine its wave function
The problem of determining a pure state vector from measurements is investigated for a quantum spin of arbitrary length. Generically, only a finite number of wave functions is compatible with the intensities of the spin components in two different spatial directions, measured by a Stern-Gerlach apparatus. The remaining ambiguity can be resolved by one additional well-defined measurement. This method combines efficiency with simplicity: only a small number of quantities have to be measured and the experimental setup is elementary. Other approaches to determine state vectors from measurements, also known as the ââPauli problem,ââ are reviewed for both spin and particle systems
Persistent Current of Free Electrons in the Plane
Predictions of Akkermans et al. are essentially changed when the Krein
spectral displacement operator is regularized by means of zeta function.
Instead of piecewise constant persistent current of free electrons on the plane
one has a current which varies linearly with the flux and is antisymmetric with
regard to all time preserving values of including . Different
self-adjoint extensions of the problem and role of the resonance are discussed.Comment: (Comment on "Relation between Persistent Currents and the Scattering
Matrix", Phys. Rev. Lett. {\bf 66}, 76 (1991)) plain latex, 4pp., IPNO/TH
94-2
Testing the assumptions of linear prediction analysis in normal vowels
This paper develops an improved surrogate data test to show experimental evidence, for all the simple vowels of US English, for both male and female speakers, that Gaussian linear prediction analysis, a ubiquitous technique in current speech technologies, cannot be used to extract all the dynamical structure of real speech time series. The test provides robust evidence undermining the validity of these linear techniques, supporting the assumptions of either dynamical nonlinearity and/or non-Gaussianity common to more recent, complex, efforts at dynamical modelling speech time series. However, an additional finding is that the classical assumptions cannot be ruled out entirely, and plausible evidence is given to explain the success of the linear Gaussian theory as a weak approximation to the true, nonlinear/non-Gaussian dynamics. This supports the use of appropriate hybrid linear/nonlinear/non-Gaussian modelling. With a calibrated calculation of statistic and particular choice of experimental protocol, some of the known systematic problems of the method of surrogate data testing are circumvented to obtain results to support the conclusions to a high level of significance
Rashba effect in 2D mesoscopic systems with transverse magnetic field
We present semiclassical and quantum mechanical results for the effects of a
strong magnetic field in Quantum Wires in the presence of Rashba Spin Orbit
coupling. Analytical and numerical results show how the perturbation acts in
the presence of a transverse magnetic field in the ballistic regime and we
assume a strong reduction of the backward scattering interaction which could
have some consequences for the Tomonaga-Luttinger transport. We analyze the
spin texture due to the action of Spin Orbit coupling and magnetic field often
referring to the semiclassical solutions that magnify the singular spin
polarization: results are obtained for free electrons in a twodimensional
electron gas and for electrons in a Quantum Wire.
We propose the systems as possible devices for the spin filtering at various
regimes.Comment: 12 pages, 12 figures, to appear in Phys. Rev.
A superconvergent representation of the Gersten-Nitzan and Ford-Webber nonradiative rates
An alternative representation of the quasistatic nonradiative rates of
Gersten and Nitzan [J. Chem. Phys. 1981, 75, 1139] and Ford and Weber [Phys.
Rep. 1984, 113, 195] is derived for the respective parallel and perpendicular
dipole orientations. Given the distance d of a dipole from a sphere surface of
radius a, the representations comprise four elementary analytic functions and a
modified multipole series taking into account residual multipole contributions.
The analytic functions could be arranged hierarchically according to decreasing
singularity at the short distance limit d ---> 0, ranging from d^{-3} over
d^{-1} to ln (d/a). The alternative representations exhibit drastically
improved convergence properties. On keeping mere residual dipole contribution
of the modified multipole series, the representations agree with the converged
rates on at least 99.9% for all distances, arbitrary particle sizes and
emission wavelengths, and for a broad range of dielectric constants. The
analytic terms of the representations reveal a complex distance dependence and
could be used to interpolate between the familiar d^{-3} short-distance and
d^{-6} long-distance behaviors with an unprecedented accuracy. Therefore, the
representations could be especially useful for the qualitative and quantitative
understanding of the distance behavior of nonradiative rates of fluorophores
and semiconductor quantum dots involving nanometal surface energy transfer in
the presence of metallic nanoparticles or nanoantennas. As a byproduct, a
complete short-distance asymptotic of the quasistatic nonradiative rates is
derived. The above results for the nonradiative rates translate
straightforwardly to the so-called image enhancement factors Delta, which are
of relevance for the surface-enhanced Raman scattering.Comment: 30 pages including 6 figure
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