3,649 research outputs found
Comments on discrete time in quantum mechanics
The possibility that time can be regarded as a discrete parameter is
re-examined. We study the dynamics of the free particle and find in some cases
superluminal propagation
Legendrian Distributions with Applications to Poincar\'e Series
Let be a compact Kahler manifold and a quantizing holomorphic
Hermitian line bundle. To immersed Lagrangian submanifolds of
satisfying a Bohr-Sommerfeld condition we associate sequences , where is a
holomorphic section of . The terms in each sequence concentrate
on , and a sequence itself has a symbol which is a half-form,
, on . We prove estimates, as , of the norm
squares in terms of . More generally, we show that if and
are two Bohr-Sommerfeld Lagrangian submanifolds intersecting
cleanly, the inner products have an
asymptotic expansion as , the leading coefficient being an integral
over the intersection . Our construction is a
quantization scheme of Bohr-Sommerfeld Lagrangian submanifolds of . We prove
that the Poincar\'e series on hyperbolic surfaces are a particular case, and
therefore obtain estimates of their norms and inner products.Comment: 41 pages, LaTe
Opinion Formation in Laggard Societies
We introduce a statistical physics model for opinion dynamics on random
networks where agents adopt the opinion held by the majority of their direct
neighbors only if the fraction of these neighbors exceeds a certain threshold,
p_u. We find a transition from total final consensus to a mixed phase where
opinions coexist amongst the agents. The relevant parameters are the relative
sizes in the initial opinion distribution within the population and the
connectivity of the underlying network. As the order parameter we define the
asymptotic state of opinions. In the phase diagram we find regions of total
consensus and a mixed phase. As the 'laggard parameter' p_u increases the
regions of consensus shrink. In addition we introduce rewiring of the
underlying network during the opinion formation process and discuss the
resulting consequences in the phase diagram.Comment: 5 pages, eps fig
Parameterized Post-Newtonian coefficients for Brans-Dicke gravity with d+1 dimensions
We present calculations of Post-Newtonian parameters for Brans-Dicke
tensor-scalar gravity in an arbitrary number of compact extra dimensions in
both the Jordan and Einstein conformal frames. We find that the parameter
gamma, which measures the amount of spacetime curvature per unit mass, becomes
a function of omega, the coefficient of the scalar kinetic term in the
Brans-Dicke Lagrangian. Experiment has placed strong constraints on gamma which
require that omega become negative in the Jordan frame for any number of extra
dimensions, highlighting that this formulation is not physical. We also confirm
the well-known result that a compact extra dimension can be equivalently viewed
as a massless scalar `dilaton.' In the Einstein frame, we find that the
behavior of gamma as constrained by experiment replicates that which is
predicted by string theory.Comment: 9 pages, accepted in Classical and Quantum Gravit
Variability of Active Galactic Nuclei from the Optical to X-ray Regions
Some progress in understanding AGN variability is reviewed. Reprocessing of
X-ray radiation to produce significant amounts of longer-wavelength continua
seems to be ruled out. In some objects where there has been correlated X-ray
and optical variability, the amplitude of the optical variability has exceeded
the amplitude of X-ray variability. We suggest that accelerated particles
striking material could be linking X-ray and optical variability (as in
activity in the solar chromosphere). Beaming effects could be significant in
all types of AGN. The diversity in optical/X-ray relationships at different
times in the same object, and between different objects, might be explained by
changes in geometry and directions of motion relative to our line of sight.
Linear shot-noise models of the variability are ruled out; instead there must
be large-scale organization of variability. Variability occurs on
light-crossing timescales rather than viscous timescales and this probably
rules out the standard Shakura-Sunyaev accretion disk. Radio-loud and
radio-quiet AGNs have similar continuum shapes and similar variability
properties. This suggests similar continuum origins and variability mechanisms.
Despite their extreme X-ray variability, narrow-line Seyfert 1s (NLS1s) do not
show extreme optical variability.Comment: Invited talk given at Euro Asian Astronomical Society meeting in
Moscow, June 2002. 20 pages, 4 figures. References update
Pluricomplex Green and Lempert functions for equally weighted poles
For a domain in , the pluricomplex Green function with
poles is defined as .
When there is only one pole, or two poles in the unit ball, it turns out to be
equal to the Lempert function defined from analytic disks into by . It is known
that we always have . In the more general case where we
allow weighted poles, there is a counterexample to equality due to Carlehed and
Wiegerinck, with equal to the bidisk.
Here we exhibit a counterexample using only four distinct equally weighted
poles in the bidisk. In order to do so, we first define a more general notion
of Lempert function "with multiplicities", analogous to the generalized Green
functions of Lelong and Rashkovskii, then we show how in some examples this can
be realized as a limit of regular Lempert functions when the poles tend to each
other. Finally, from an example where in the case of
multiple poles, we deduce that distinct (but close enough) equally weighted
poles will provide an example of the same inequality. Open questions are
pointed out about the limits of Green and Lempert functions when poles tend to
each other.Comment: 25 page
Complexity, transparency and time pressure: practical insights into science communication in times of crisis
A global crisis such as the COVID-19 pandemic that started in early 2020 poses significant challenges for how research is conducted and communicated. We present four case studies from the perspective of an interdisciplinary research institution that switched to âcorona-modeâ during the first two months of the crisis, focussing all its capacities on COVID-19-related issues, communicating to the public directly and via media, as well as actively advising the national government. The case studies highlight the challenges posed by the increased time pressure, high demand for transparency, and communication of complexity and uncertainty. The article gives insights into how these challenges were addressed in our research institution and how science communication in general can be managed during a crisis
Can a matter-dominated model with constant bulk viscosity drive the accelerated expansion of the universe?
We test a cosmological model which the only component is a pressureless fluid
with a constant bulk viscosity as an explanation for the present accelerated
expansion of the universe. We classify all the possible scenarios for the
universe predicted by the model according to their past, present and future
evolution and we test its viability performing a Bayesian statistical analysis
using the SCP ``Union'' data set (307 SNe Ia), imposing the second law of
thermodynamics on the dimensionless constant bulk viscous coefficient \zeta and
comparing the predicted age of the universe by the model with the constraints
coming from the oldest globular clusters.
The best estimated values found for \zeta and the Hubble constant Ho are:
\zeta=1.922 \pm 0.089 and Ho=69.62 \pm 0.59 km/s/Mpc with a \chi^2=314. The age
of the universe is found to be 14.95 \pm 0.42 Gyr. We see that the estimated
value of Ho as well as of \chi^2 are very similar to those obtained from LCDM
model using the same SNe Ia data set. The estimated age of the universe is in
agreement with the constraints coming from the oldest globular clusters.
Moreover, the estimated value of \zeta is positive in agreement with the second
law of thermodynamics (SLT).
On the other hand, we perform different forms of marginalization over the
parameter Ho in order to study the sensibility of the results to the way how Ho
is marginalized. We found that it is almost negligible the dependence between
the best estimated values of the free parameters of this model and the way how
Ho is marginalized in the present work. Therefore, this simple model might be a
viable candidate to explain the present acceleration in the expansion of the
universe.Comment: 31 pages, 12 figures and 2 tables. Accepted to be published in the
Journal of Cosmology and Astroparticle Physics. Analysis using the new SCP
"Union" SNe Ia dataset instead of the Gold 2006 and ESSENCE datasets and
without changes in the conclusions. Added references. Related works:
arXiv:0801.1686 and arXiv:0810.030
Bianchi Type I Magnetofluid Cosmological Models with Variable Cosmological Constant Revisited
The behaviour of magnetic field in anisotropic Bianchi type I cosmological
model for bulk viscous distribution is investigated. The distribution consists
of an electrically neutral viscous fluid with an infinite electrical
conductivity. It is assumed that the component of shear tensor
is proportional to expansion () and the coefficient of
bulk viscosity is assumed to be a power function of mass density. Some physical
and geometrical aspects of the models are also discussed in presence and also
in absence of the magnetic field.Comment: 13 page
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