11,213 research outputs found
Angular spectrum of quantized light beams
We introduce a generalized angular spectrum representation for quantized
light beams. By using our formalism, we are able to derive simple expressions
for the electromagnetic vector potential operator in the case of: {a)}
time-independent paraxial fields, {b)} time-dependent paraxial fields, and {c)}
non-paraxial fields. For the first case, the well known paraxial results are
fully recovered.Comment: 3 pages, no figure
Why bayesian “evidence for H1” in one condition and bayesian “evidence for H0” in another condition does not mean good-enough bayesian evidence for a difference between the conditions
Psychologists are often interested in whether an independent variable has a different effect in condition A than in condition B. To test such a question, one needs to directly compare the effect of that variable in the two conditions (i.e., test the interaction). Yet many researchers tend to stop when they find a significant test in one condition and a nonsignificant test in the other condition, deeming this as sufficient evidence for a difference between the two conditions. In this Tutorial, we aim to raise awareness of this inferential mistake when Bayes factors are used with conventional cutoffs to draw conclusions. For instance, some researchers might falsely conclude that there must be good-enough evidence for the interaction if they find good-enough Bayesian evidence for the alternative hypothesis, H1, in condition A and good-enough Bayesian evidence for the null hypothesis, H0, in condition B. The case study we introduce highlights that ignoring the test of the interaction can lead to unjustified conclusions and demonstrates that the principle that any assertion about the existence of an interaction necessitates the direct comparison of the conditions is as true for Bayesian as it is for frequentist statistics. We provide an R script of the analyses of the case study and a Shiny app that can be used with a 2 Ă— 2 design to develop intuitions on this issue, and we introduce a rule of thumb with which one can estimate the sample size one might need to have a well-powered design
Spin Precession and Avalanches
In many magnetic materials, spin dynamics at short times are dominated by
precessional motion as damping is relatively small. In the limit of no damping
and no thermal noise, we show that for a large enough initial instability, an
avalanche can transition to an ergodic phase where the state is equivalent to
one at finite temperature, often above that for ferromagnetic ordering. This
dynamical nucleation phenomenon is analyzed theoretically. For small finite
damping the high temperature growth front becomes spread out over a large
region. The implications for real materials are discussed.Comment: 4 pages 2 figure
On the error statistics of Viterbi decoding and the performance of concatenated codes
Computer simulation results are presented on the performance of convolutional codes of constraint lengths 7 and 10 concatenated with the (255, 223) Reed-Solomon code (a proposed NASA standard). These results indicate that as much as 0.8 dB can be gained by concatenating this Reed-Solomon code with a (10, 1/3) convolutional code, instead of the (7, 1/2) code currently used by the DSN. A mathematical model of Viterbi decoder burst-error statistics is developed and is validated through additional computer simulations
Measurement of conditional phase shifts for quantum logic
Measurements of the birefringence of a single atom strongly coupled to a
high-finesse optical resonator are reported, with nonlinear phase shifts
observed for intracavity photon number much less than one. A proposal to
utilize the measured conditional phase shifts for implementing quantum logic
via a quantum-phase gate (QPG) is considered. Within the context of a simple
model for the field transformation, the parameters of the "truth table" for the
QPG are determined.Comment: 4 pages in Postscript format, including 4 figures (attached as
uuencoded version of a gzip-file
Mechanism for nonequilibrium symmetry breaking and pattern formation in magnetic films
Magnetic thin films exhibit a strong variation in properties depending on
their degree of disorder. Recent coherent x-ray speckle experiments on magnetic
films have measured the loss of correlation between configurations at opposite
fields and at the same field, upon repeated field cycling. We perform finite
temperature numerical simulations on these systems that provide a comprehensive
explanation for the experimental results. The simulations demonstrate, in
accordance with experiments, that the memory of configurations increases with
film disorder. We find that non-trivial microscopic differences exist between
the zero field spin configuration obtained by starting from a large positive
field and the zero field configuration starting at a large negative field. This
seemingly paradoxical beahvior is due to the nature of the vector spin dynamics
and is also seen in the experiments. For low disorder, there is an instability
which causes the spontaneous growth of line-like domains at a critical field,
also in accord with experiments. It is this unstable growth, which is highly
sensitive to thermal noise, that is responsible for the small correlation
between patterns under repeated cycling. The domain patterns, hysteresis loops,
and memory properties of our simulated systems match remarkably well with the
real experimental systems.Comment: 12 pages, 10 figures Added comparison of results with
cond-mat/0412461 and some more discussio
Why one-size-fits-all vaso-modulatory interventions fail to control glioma invasion: in silico insights
There is an ongoing debate on the therapeutic potential of vaso-modulatory
interventions against glioma invasion. Prominent vasculature-targeting
therapies involve functional tumour-associated blood vessel deterioration and
normalisation. The former aims at tumour infarction and nutrient deprivation
medi- ated by vascular targeting agents that induce occlusion/collapse of
tumour blood vessels. In contrast, the therapeutic intention of normalising the
abnormal structure and function of tumour vascular net- works, e.g. via
alleviating stress-induced vaso-occlusion, is to improve chemo-, immuno- and
radiation therapy efficacy. Although both strategies have shown therapeutic
potential, it remains unclear why they often fail to control glioma invasion
into the surrounding healthy brain tissue. To shed light on this issue, we
propose a mathematical model of glioma invasion focusing on the interplay
between the mi- gration/proliferation dichotomy (Go-or-Grow) of glioma cells
and modulations of the functional tumour vasculature. Vaso-modulatory
interventions are modelled by varying the degree of vaso-occlusion. We
discovered the existence of a critical cell proliferation/diffusion ratio that
separates glioma invasion re- sponses to vaso-modulatory interventions into two
distinct regimes. While for tumours, belonging to one regime, vascular
modulations reduce the tumour front speed and increase the infiltration width,
for those in the other regime the invasion speed increases and infiltration
width decreases. We show how these in silico findings can be used to guide
individualised approaches of vaso-modulatory treatment strategies and thereby
improve success rates
Mean-field analysis of a dynamical phase transition in a cellular automaton model for collective motion
A cellular automaton model is presented for random walkers with biologically
motivated interactions favoring local alignment and leading to collective
motion or swarming behavior. The degree of alignment is controlled by a
sensitivity parameter, and a dynamical phase transition exhibiting spontaneous
breaking of rotational symmetry occurs at a critical parameter value. The model
is analyzed using nonequilibrium mean field theory: Dispersion relations for
the critical modes are derived, and a phase diagram is constructed. Mean field
predictions for the two critical exponents describing the phase transition as a
function of sensitivity and density are obtained analytically.Comment: 4 pages, 4 figures, final version as publishe
Experimental application of decoherence-free subspaces in a quantum-computing algorithm
For a practical quantum computer to operate, it will be essential to properly
manage decoherence. One important technique for doing this is the use of
"decoherence-free subspaces" (DFSs), which have recently been demonstrated.
Here we present the first use of DFSs to improve the performance of a quantum
algorithm. An optical implementation of the Deutsch-Jozsa algorithm can be made
insensitive to a particular class of phase noise by encoding information in the
appropriate subspaces; we observe a reduction of the error rate from 35% to
essentially its pre-noise value of 8%.Comment: 11 pages, 4 figures, submitted to PR
General Relativistic Effect of Gravitomagnetic Charge on Pulsar Magnetosphere and Particle Acceleration in a Polar Cap
We study magnetospheric structure surrounding rotating magnetized neutron
star with nonvanishing NUT (Newman-Tamburino-Unti) parameter. For the
simplicity of calculations Goldreich-Julian charge density is analyzed for the
aligned neutron star with zero inclination between magnetic field,
gravitomagnetic field and rotation axis. From the system of Maxwell equations
in spacetime of slowly rotating NUT star, second-order differential equation
for electrostatic potential is derived. Analytical solution of this equation
indicates the general relativistic modification of an accelerating electric
field and charge density along the open field lines by the gravitomagnetic
charge. The implication of this effect to the magnetospheric energy loss
problem is underlined. In the second part of the paper we derive the equations
of motion of test particles in magnetosphere of slowly rotating NUT star. Then
we analyze particle motion in the polar cap and show that NUT parameter can
significantly change conditions for particle acceleration.Comment: 21 pages, 6 figures, accepted for publication in Ap
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