5,368 research outputs found
Characterisation and representation of non-dissipative electromagnetic medium with a double light cone
We study Maxwell's equations on a 4-manifold N with a medium that is
non-dissipative and has a linear and pointwise response. In this setting, the
medium can be represented by a suitable (2,2)-tensor on the 4-manifold N.
Moreover, in each cotangent space on N, the medium defines a Fresnel surface.
Essentially, the Fresnel surface is a tensorial analogue of the dispersion
equation that describes the response of the medium for signals in the geometric
optics limit. For example, in isotropic medium the Fresnel surface is at each
point a Lorentz light cone. In a recent paper, I. Lindell, A. Favaro and L.
Bergamin introduced a condition that constrains the polarisation for plane
waves. In this paper we show (under suitable assumptions) that a slight
strengthening of this condition gives a pointwise characterisation of all
medium tensors for which the Fresnel surface is the union of two distinct
Lorentz null cones. This is for example the behaviour of uniaxial medium like
calcite. Moreover, using the representation formulas from Lindell et al. we
obtain a closed form representation formula that pointwise parameterises all
medium tensors for which the Fresnel surface is the union of two distinct
Lorentz null cones. Both the characterisation and the representation formula
are tensorial and do not depend on local coordinates
Extreme points of the set of density matrices with positive partial transpose
We present a necessary and sufficient condition for a finite dimensional
density matrix to be an extreme point of the convex set of density matrices
with positive partial transpose with respect to a subsystem. We also give an
algorithm for finding such extreme points and illustrate this by some examples.Comment: 4 pages, 2 figure
Statistical properties of Klauder-Perelomov coherent states for the Morse potential
We present in this paper a realistic construction of the coherent states for
the Morse potential using the Klauder-Perelomov approach . We discuss the
statistical properties of these states, by deducing the Q- and P-distribution
functions. The thermal expectations for the quantum canonical ideal gas of the
Morse oscillators are also calculated
Millimeter Wave Localization: Slow Light and Enhanced Absorption
We exploit millimeter wave technology to measure the reflection and
transmission response of random dielectric media. Our samples are easily
constructed from random stacks of identical, sub-wavelength quartz and Teflon
wafers. The measurement allows us to observe the characteristic transmission
resonances associated with localization. We show that these resonances give
rise to enhanced attenuation even though the attenuation of homogeneous quartz
and Teflon is quite low. We provide experimental evidence of disorder-induced
slow light and superluminal group velocities, which, in contrast to photonic
crystals, are not associated with any periodicity in the system. Furthermore,
we observe localization even though the sample is only about four times the
localization length, interpreting our data in terms of an effective cavity
model. An algorithm for the retrieval of the internal parameters of random
samples (localization length and average absorption rate) from the external
measurements of the reflection and transmission coefficients is presented and
applied to a particular random sample. The retrieved value of the absorption is
in agreement with the directly measured value within the accuracy of the
experiment.Comment: revised and expande
Switching dynamics of surface stabilized ferroelectric liquid crystal cells: effects of anchoring energy asymmetry
We study both theoretically and experimentally switching dynamics in surface
stabilized ferroelectric liquid crystal cells with asymmetric boundary
conditions. In these cells the bounding surfaces are treated differently to
produce asymmetry in their anchoring properties. Our electro-optic measurements
of the switching voltage thresholds that are determined by the peaks of the
reversal polarization current reveal the frequency dependent shift of the
hysteresis loop. We examine the predictions of the uniform dynamical model with
the anchoring energy taken into account. It is found that the asymmetry effects
are dominated by the polar contribution to the anchoring energy. Frequency
dependence of the voltage thresholds is studied by analyzing the properties of
time-periodic solutions to the dynamical equation (cycles). For this purpose,
we apply the method that uses the parameterized half-period mappings for the
approximate model and relate the cycles to the fixed points of the composition
of two half-period mappings. The cycles are found to be unstable and can only
be formed when the driving frequency is lower than its critical value. The
polar anchoring parameter is estimated by making a comparison between the
results of modelling and the experimental data for the shift vs frequency
curve. For a double-well potential considered as a deformation of the
Rapini-Papoular potential, the branch of stable cycles emerges in the low
frequency region separated by the gap from the high frequency interval for
unstable cycles.Comment: 35 pages, 15 figure
- …