47,146 research outputs found
Gradient of the Casimir force between Au surfaces of a sphere and a plate measured using atomic force microscope in a frequency shift technique
We present measurement results for the gradient of the Casimir force between
an Au-coated sphere and an Au-coated plate obtained by means of an atomic force
microscope operated in a frequency shift technique. This experiment was
performed at a pressure of 3x10^{-8} Torr with hollow glass sphere of 41.3 mcm
radius. Special attention is paid to electrostatic calibrations including the
problem of electrostatic patches. All calibration parameters are shown to be
separation-independent after the corrections for mechanical drift are included.
The gradient of the Casimir force was measured in two ways with applied
compensating voltage to the plate and with different applied voltages and
subsequent subtraction of electric forces. The obtained mean gradients are
shown to be in mutual agreement and in agreement with previous experiments
performed using a micromachined oscillator. The obtained data are compared with
theoretical predictions of the Lifshitz theory including corrections beyond the
proximity force approximation. An independent comparison with no fitting
parameters demonstrated that the Drude model approach is excluded by the data
at a 67% confidence level over the separation region from 235 to 420 nm. The
theoretical approach using the generalized plasma-like model is shown to be
consistent with the data over the entire measurement range. Corrections due to
the nonlinearity of oscillator are calculated and the application region of the
linear regime is determined. A conclusion is made that the results of several
performed experiments call for a thorough analysis of the basics of the theory
of dispersion forces.Comment: 35 pages, 14 figures, 1 table; to appear in Phys. Rev.
Instabilities and Non-Reversibility of Molecular Dynamics Trajectories
The theoretical justification of the Hybrid Monte Carlo algorithm depends
upon the molecular dynamics trajectories within it being exactly reversible. If
computations were carried out with exact arithmetic then it would be easy to
ensure such reversibility, but the use of approximate floating point arithmetic
inevitably introduces violations of reversibility. In the absence of evidence
to the contrary, we are usually prepared to accept that such rounding errors
can be made small enough to be innocuous, but in certain circumstances they are
exponentially amplified and lead to blatantly erroneous results. We show that
there are two types of instability of the molecular dynamics trajectories which
lead to this behavior, instabilities due to insufficiently accurate numerical
integration of Hamilton's equations, and intrinsic chaos in the underlying
continuous fictitious time equations of motion themselves. We analyze the
former for free field theory, and show that it is essentially a finite volume
effect. For the latter we propose a hypothesis as to how the Liapunov exponent
describing the chaotic behavior of the fictitious time equations of motion for
an asymptotically free quantum field theory behaves as the system is taken to
its continuum limit, and explain why this means that instabilities in molecular
dynamics trajectories are not a significant problem for Hybrid Monte Carlo
computations. We present data for pure gauge theory and for QCD with
dynamical fermions on small lattices to illustrate and confirm some of our
results.Comment: 28 pages latex with 19 color postscript figures included by eps
Comparison of the experimental data for the Casimir pressure with the Lifshitz theory at zero temperature
We perform detailed comparison of the experimental data of the experiment on
the determination of the Casimir pressure between two parallel Au plates with
the theoretical values computed using the Lifshitz formula at zero temperature.
Computations are done using the optical data for the complex index of
refraction of Au extrapolated to low frequencies by means of the Drude model
with both most often used and other suggested Drude parameters. It is shown
that the experimental data exclude the Lifshitz formula at zero temperature at
a 70% confidence level if the Drude model with most often used values of the
parameters is employed. If other values of the Drude parameters are used, the
Lifshitz formula at zero frequency is experimentally excluded at a 95%
confidence level. The Lifshitz formula at zero temperature combined with the
generalized plasma-like model with most often used value of the plasma
frequency is shown to be experimentally consistent. We propose a decisive
experiment which will shed additional light on the role of relaxation
properties of conduction electrons in the Casimir effect.Comment: 22 pages, 6 figures; Phys. Rev. B, to appea
On the accuracy of language trees
Historical linguistics aims at inferring the most likely language
phylogenetic tree starting from information concerning the evolutionary
relatedness of languages. The available information are typically lists of
homologous (lexical, phonological, syntactic) features or characters for many
different languages.
From this perspective the reconstruction of language trees is an example of
inverse problems: starting from present, incomplete and often noisy,
information, one aims at inferring the most likely past evolutionary history. A
fundamental issue in inverse problems is the evaluation of the inference made.
A standard way of dealing with this question is to generate data with
artificial models in order to have full access to the evolutionary process one
is going to infer. This procedure presents an intrinsic limitation: when
dealing with real data sets, one typically does not know which model of
evolution is the most suitable for them. A possible way out is to compare
algorithmic inference with expert classifications. This is the point of view we
take here by conducting a thorough survey of the accuracy of reconstruction
methods as compared with the Ethnologue expert classifications. We focus in
particular on state-of-the-art distance-based methods for phylogeny
reconstruction using worldwide linguistic databases.
In order to assess the accuracy of the inferred trees we introduce and
characterize two generalizations of standard definitions of distances between
trees. Based on these scores we quantify the relative performances of the
distance-based algorithms considered. Further we quantify how the completeness
and the coverage of the available databases affect the accuracy of the
reconstruction. Finally we draw some conclusions about where the accuracy of
the reconstructions in historical linguistics stands and about the leading
directions to improve it.Comment: 36 pages, 14 figure
Making precise predictions of the Casimir force between metallic plates via a weighted Kramers-Kronig transform
The possibility of making precise predictions for the Casimir force is
essential for the theoretical interpretation of current precision experiments
on the thermal Casimir effect with metallic plates, especially for sub-micron
separations. For this purpose it is necessary to estimate very accurately the
dielectric function of a conductor along the imaginary frequency axis. This
task is complicated in the case of ohmic conductors, because optical data do
not usually extend to sufficiently low frequencies to permit an accurate
evaluation of the standard Kramers-Kronig integral used to compute . By making important improvements in the results of a previous paper by
the author, it is shown that this difficulty can be resolved by considering
suitable weighted dispersions relations, which strongly suppress the
contribution of low frequencies. The weighted dispersion formulae presented in
this paper permit to estimate accurately the dielectric function of ohmic
conductors for imaginary frequencies, on the basis of optical data extending
from the IR to the UV, with no need of uncontrolled data extrapolations towards
zero frequency that are instead necessary with standard Kramers-Kronig
relations. Applications to several sets of data for gold films are presented to
demonstrate viability of the new dispersion formulae.Comment: 18 pages, 15 encapsulated figures. In the revised version important
improvements have been made, which affect the main conclusions of the pape
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