1,408 research outputs found
On the Brownian gas: a field theory with a Poissonian ground state
As a first step towards a successful field theory of Brownian particles in
interaction, we study exactly the non-interacting case, its combinatorics and
its non-linear time-reversal symmetry. Even though the particles do not
interact, the field theory contains an interaction term: the vertex is the
hallmark of the original particle nature of the gas and it enforces the
constraint of a strictly positive density field, as opposed to a Gaussian free
field. We compute exactly all the n-point density correlation functions,
determine non-perturbatively the Poissonian nature of the ground state and
emphasize the futility of any coarse-graining assumption for the derivation of
the field theory. We finally verify explicitly, on the n-point functions, the
fluctuation-dissipation theorem implied by the time-reversal symmetry of the
action.Comment: 31 page
Geomagnetic induction and conductive structures in north-west India
Magnetic disturbance events and quiet daily variation as recorded by the 1979 magnetometer array study in north-west India are analysed for evidence of electrical conductivity structures in the region. Contour maps of Fourier transform parameters are presented, and the disturbance event data are also reduced to sets of real and quadrature Parkinson arrows over a range of periods. A variety of conductive structures in the area are mapped, including some relatively shallow ones thought to be caused by sediments, as in the Ganga basin. More information is obtained on a major conductivity structure which strikes perpendicular to the Ganga basin into the foothills of the Himalayas; a second major conductivity structure is detected to lie to the west of the array area, and may be associated there with some aspect of the suture zone of India and Asia
Masses, Luminosities, and Orbital Coplanarities of the mu Orionis Quadruple Star System from PHASES Differential Astrometry
mu Orionis was identified by spectroscopic studies as a quadruple star
system. Seventeen high precision differential astrometry measurements of mu Ori
have been collected by the Palomar High-precision Astrometric Search for
Exoplanet Systems (PHASES). These show both the motion of the long period
binary orbit and short period perturbations superimposed on that caused by each
of the components in the long period system being themselves binaries. The new
measurements enable the orientations of the long period binary and short period
subsystems to be determined. Recent theoretical work predicts the distribution
of relative inclinations between inner and outer orbits of hierarchical systems
to peak near 40 and 140 degrees. The degree of coplanarity of this complex
system is determined, and the angle between the planes of the A-B and Aa-Ab
orbits is found to be 136.7 +/- 8.3 degrees, near the predicted distribution
peak at 140 degrees; this result is discussed in the context of the handful of
systems with established mutual inclinations. The system distance and masses
for each component are obtained from a combined fit of the PHASES astrometry
and archival radial velocity observations. The component masses have relative
precisions of 5% (component Aa), 15% (Ab), and 1.4% (each of Ba and Bb). The
median size of the minor axes of the uncertainty ellipses for the new
measurements is 20 micro-arcseconds. Updated orbits for delta Equulei, kappa
Pegasi, and V819 Herculis are also presented.Comment: 12 Pages, Accepted for publication in A
Analytic approach to stochastic cellular automata: exponential and inverse power distributions out of Random Domino Automaton
Inspired by extremely simplified view of the earthquakes we propose the
stochastic domino cellular automaton model exhibiting avalanches. From
elementary combinatorial arguments we derive a set of nonlinear equations
describing the automaton. Exact relations between the average parameters of the
model are presented. Depending on imposed triggering, the model reproduces both
exponential and inverse power statistics of clusters.Comment: improved, new material added; 9 pages, 3 figures, 2 table
Central factorials under the Kontorovich-Lebedev transform of polynomials
We show that slight modifications of the Kontorovich-Lebedev transform lead
to an automorphism of the vector space of polynomials. This circumstance along
with the Mellin transformation property of the modified Bessel functions
perform the passage of monomials to central factorial polynomials. A special
attention is driven to the polynomial sequences whose KL-transform is the
canonical sequence, which will be fully characterized. Finally, new identities
between the central factorials and the Euler polynomials are found.Comment: also available at http://cmup.fc.up.pt/cmup/ since the 2nd August
201
Hall Normalization Constants for the Bures Volumes of the n-State Quantum Systems
We report the results of certain integrations of quantum-theoretic interest,
relying, in this regard, upon recently developed parameterizations of Boya et
al of the n x n density matrices, in terms of squared components of the unit
(n-1)-sphere and the n x n unitary matrices. Firstly, we express the normalized
volume elements of the Bures (minimal monotone) metric for n = 2 and 3,
obtaining thereby "Bures prior probability distributions" over the two- and
three-state systems. Then, as an essential first step in extending these
results to n > 3, we determine that the "Hall normalization constant" (C_{n})
for the marginal Bures prior probability distribution over the
(n-1)-dimensional simplex of the n eigenvalues of the n x n density matrices
is, for n = 4, equal to 71680/pi^2. Since we also find that C_{3} = 35/pi, it
follows that C_{4} is simply equal to 2^{11} C_{3}/pi. (C_{2} itself is known
to equal 2/pi.) The constant C_{5} is also found. It too is associated with a
remarkably simple decompositon, involving the product of the eight consecutive
prime numbers from 2 to 23.
We also preliminarily investigate several cases, n > 5, with the use of
quasi-Monte Carlo integration. We hope that the various analyses reported will
prove useful in deriving a general formula (which evidence suggests will
involve the Bernoulli numbers) for the Hall normalization constant for
arbitrary n. This would have diverse applications, including quantum inference
and universal quantum coding.Comment: 14 pages, LaTeX, 6 postscript figures. Revised version to appear in
J. Phys. A. We make a few slight changes from the previous version, but also
add a subsection (III G) in which several variations of the basic problem are
newly studied. Rather strong evidence is adduced that the Hall constants are
related to partial sums of denominators of the even-indexed Bernoulli
numbers, although a general formula is still lackin
Long-Term Changes in Physical Activity Following a One-Year Home-Based Physical Activity Counseling Program in Older Adults with Multiple Morbidities
This study assessed the sustained effect of a physical activity (PA) counseling intervention on PA one year after intervention, predictors of sustained PA participation, and three classes of post-intervention PA trajectories (improvers, maintainers, and decliners) in 238 older Veterans. Declines in minutes of PA from 12 to 24 months were observed for both the treatment and control arms of the study. PA at 12 months was the strongest predictor of post-intervention changes in PA. To our surprise, those who took up the intervention and increased PA levels the most, had significant declines in post-intervention PA. Analysis of the three post-intervention PA trajectories demonstrated that the maintenance group actually reflected a group of nonresponders to the intervention who had more comorbidities, lower self-efficacy, and worse physical function than the improvers or decliners. Results suggest that behavioral counseling/support must be ongoing to promote maintenance. Strategies to promote PA appropriately to subgroups of individuals are needed
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