1,983 research outputs found
Quantum limits in interferometric measurements
Quantum noise limits the sensitivity of interferometric measurements. It is
generally admitted that it leads to an ultimate sensitivity, the ``standard
quantum limit''. Using a semi-classical analysis of quantum noise, we show that
a judicious use of squeezed states allows one in principle to push the
sensitivity beyond this limit. This general method could be applied to large
scale interferometers designed for gravitational wave detection.Comment: 4 page
Microscopic approach of a time elapsed neural model
The spike trains are the main components of the information processing in the
brain. To model spike trains several point processes have been investigated in
the literature. And more macroscopic approaches have also been studied, using
partial differential equation models. The main aim of the present article is to
build a bridge between several point processes models (Poisson, Wold, Hawkes)
that have been proved to statistically fit real spike trains data and
age-structured partial differential equations as introduced by Pakdaman,
Perthame and Salort
Radiative heat transfer between two dielectric nanogratings in the scattering approach
We present a theoretical study of radiative heat transfer between dielectric
nanogratings in the scattering approach. As a comparision with these exact
results, we also evaluate the domain of validity of Derjaguin's Proximity
Approximation (PA). We consider a system of two corrugated silica plates with
various grating geometries, separation distances, and lateral displacement of
the plates with respect to one another. Numerical computations show that while
the PA is a good approximation for aligned gratings, it cannot be used when the
gratings are laterally displaced. We illustrate this by a thermal modulator
device for nanosystems based on such a displacement
Group Analysis of Self-organizing Maps based on Functional MRI using Restricted Frechet Means
Studies of functional MRI data are increasingly concerned with the estimation
of differences in spatio-temporal networks across groups of subjects or
experimental conditions. Unsupervised clustering and independent component
analysis (ICA) have been used to identify such spatio-temporal networks. While
these approaches have been useful for estimating these networks at the
subject-level, comparisons over groups or experimental conditions require
further methodological development. In this paper, we tackle this problem by
showing how self-organizing maps (SOMs) can be compared within a Frechean
inferential framework. Here, we summarize the mean SOM in each group as a
Frechet mean with respect to a metric on the space of SOMs. We consider the use
of different metrics, and introduce two extensions of the classical sum of
minimum distance (SMD) between two SOMs, which take into account the
spatio-temporal pattern of the fMRI data. The validity of these methods is
illustrated on synthetic data. Through these simulations, we show that the
three metrics of interest behave as expected, in the sense that the ones
capturing temporal, spatial and spatio-temporal aspects of the SOMs are more
likely to reach significance under simulated scenarios characterized by
temporal, spatial and spatio-temporal differences, respectively. In addition, a
re-analysis of a classical experiment on visually-triggered emotions
demonstrates the usefulness of this methodology. In this study, the
multivariate functional patterns typical of the subjects exposed to pleasant
and unpleasant stimuli are found to be more similar than the ones of the
subjects exposed to emotionally neutral stimuli. Taken together, these results
indicate that our proposed methods can cast new light on existing data by
adopting a global analytical perspective on functional MRI paradigms.Comment: 23 pages, 5 figures, 4 tables. Submitted to Neuroimag
Does an atom interferometer test the gravitational redshift at the Compton frequency ?
Atom interferometers allow the measurement of the acceleration of freely
falling atoms with respect to an experimental platform at rest on Earth's
surface. Such experiments have been used to test the universality of free fall
by comparing the acceleration of the atoms to that of a classical freely
falling object. In a recent paper, M\"uller, Peters and Chu [Nature {\bf 463},
926-929 (2010)] argued that atom interferometers also provide a very accurate
test of the gravitational redshift when considering the atom as a clock
operating at the Compton frequency associated with the rest mass. We analyze
this claim in the frame of general relativity and of different alternative
theories. We show that the difference of "Compton phases" between the two paths
of the interferometer is actually zero in a large class of theories, including
general relativity, all metric theories of gravity, most non-metric theories
and most theoretical frameworks used to interpret the violations of the
equivalence principle. Therefore, in most plausible theoretical frameworks,
there is no redshift effect and atom interferometers only test the universality
of free fall. We also show that frameworks in which atom interferometers would
test the redshift pose serious problems, such as (i) violation of the Schiff
conjecture, (ii) violation of the Feynman path integral formulation of quantum
mechanics and of the principle of least action for matter waves, (iii)
violation of energy conservation, and more generally (iv) violation of the
particle-wave duality in quantum mechanics. Standard quantum mechanics is no
longer valid in such frameworks, so that a consistent interpretation of the
experiment would require an alternative formulation of quantum mechanics. As
such an alternative has not been proposed to date, we conclude that the
interpretation of atom interferometers as testing the gravitational redshift is
unsound.Comment: 26 pages. Modified version to appear in Classical and Quantum Gravit
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