2,302 research outputs found
Duration problem: basic concept and some extensions
We consider a sequence of independent random variables with the known
distribution observed sequentially. The observation is assumed to be a
value of one order statistics such as s:n-th, where 1 is less than s is less
than n. It the instances following the th observation it may remain of the
s:m or it will be the value of the order statistics r:m (of m> n observations).
Changing the rank of the observation, along with expanding a set of
observations there is a random phenomenon that is difficult to predict. From
practical reasons it is of great interest. Among others, we pose the question
of the moment in which the observation appears and whose rank will not change
significantly until the end of sampling of a certain size. We also attempt to
answer which observation should be kept to have the "good quality observation"
as long as possible. This last question was analysed by Ferguson, Hardwick and
Tamaki (1991) in the abstract form which they called the problem of duration.
This article gives a systematical presentation of the known duration models
and a new modifications. We collect results from different papers on the
duration of the extremal observation in the no-information (denoted as rank
based) case and the full-information case. In the case of non-extremal
observation duration models the most appealing are various settings related to
the two extremal order statistics. In the no-information case it will be the
maximizing duration of owning the relatively best or the second best object.
The idea was formulated and the problem was solved by Szajowski and Tamaki
(2006). The full-information duration problem with special requirement was
presented by Kurushima and Ano (2010)
Anisotropic Inflation from Extra Dimensions
Vacuum multidimensional cosmological models with internal spaces being
compact -dimensional Lie group manifolds are considered. Products of
3-spheres and manifold (a novelty in cosmology) are studied. It turns
out that the dynamical evolution of the internal space drives an accelerated
expansion of the external world (power law inflation). This generic solution
(attractor in a phase space) is determined by the Lie group space without any
fine tuning or arbitrary inflaton potentials. Matter in the four dimensions
appears in the form of a number of scalar fields representing anisotropic scale
factors for the internal space. Along the attractor solution the volume of the
internal space grows logarithmically in time. This simple and natural model
should be completed by mechanisms terminating the inflationary evolution and
transforming the geometric scalar fields into ordinary particles.Comment: LaTeX, 11 pages, 5 figures available via fax on request to
[email protected], submitted to Phys. Lett.
Dispersion of particles in an infinite-horizon Lorentz gas
We consider a two-dimensional Lorentz gas with infinite horizon. This
paradigmatic model consists of pointlike particles undergoing elastic
collisions with fixed scatterers arranged on a periodic lattice. It was
rigorously shown that when , the distribution of particles is
Gaussian. However, the convergence to this limit is ultraslow, hence it is
practically unattainable. Here we obtain an analytical solution for the Lorentz
gas' kinetics on physically relevant timescales, and find that the density in
its far tails decays as a universal power law of exponent . We also show
that the arrangement of scatterers is imprinted in the shape of the
distribution.Comment: Article with supplemental material: 10 pages, 4 figure
Black holes in the quantum universe
A succinct summary is given of the problem of reconciling observation of
black hole-like objects with quantum mechanics. If quantum black holes behave
like subsystems, and also decay, their information must be transferred to their
environments. Interactions that accomplish this with `minimal' departure from a
standard description are parameterized. Possible sensitivity of gravitational
wave or very long baseline interferometric observations to these interactions
is briefly outlined.Comment: 11 pages + ref
The local and global geometrical aspects of the twin paradox in static spacetimes: II. Reissner--Nordstr\"{o}m and ultrastatic metrics
This is a consecutive paper on the timelike geodesic structure of static
spherically symmetric spacetimes. First we show that for a stable circular
orbit (if it exists) in any of these spacetimes all the infinitesimally close
to it timelike geodesics constructed with the aid of the general geodesic
deviation vector have the same length between a pair of conjugate points. In
Reissner--Nordstr\"{o}m black hole metric we explicitly find the Jacobi fields
on the radial geodesics and show that they are locally (and globally) maximal
curves between any pair of their points outside the outer horizon. If a radial
and circular geodesics in R--N metric have common endpoints, the radial one is
longer. If a static spherically symmetric spacetime is ultrastatic, its
gravitational field exerts no force on a free particle which may stay at rest;
the free particle in motion has a constant velocity (in this sense the motion
is uniform) and its total energy always exceeds the rest energy, i.~e.~it has
no gravitational energy. Previously the absence of the gravitational force has
been known only for the global Barriola--Vilenkin monopole. In the spacetime of
the monopole we explicitly find all timelike geodesics, the Jacobi fields on
them and the condition under which a generic geodesic may have conjugate
points
The Pivotal Role of Causality in Local Quantum Physics
In this article an attempt is made to present very recent conceptual and
computational developments in QFT as new manifestations of old and well
establihed physical principles. The vehicle for converting the
quantum-algebraic aspects of local quantum physics into more classical
geometric structures is the modular theory of Tomita. As the above named
laureate to whom I have dedicated has shown together with his collaborator for
the first time in sufficient generality, its use in physics goes through
Einstein causality. This line of research recently gained momentum when it was
realized that it is not only of structural and conceptual innovative power (see
section 4), but also promises to be a new computational road into
nonperturbative QFT (section 5) which, picturesquely speaking, enters the
subject on the extreme opposite (noncommutative) side.Comment: This is a updated version which has been submitted to Journal of
Physics A, tcilatex 62 pages. Adress: Institut fuer Theoretische Physik
FU-Berlin, Arnimallee 14, 14195 Berlin presently CBPF, Rua Dr. Xavier Sigaud
150, 22290-180 Rio de Janeiro, Brazi
New Concepts in Particle Physics from Solution of an Old Problem
Recent ideas on modular localization in local quantum physics are used to
clarify the relation between on- and off-shell quantities in particle physics;
in particular the relation between on-shell crossing symmetry and off-shell
Einstein causality. Among the collateral results of this new nonperturbative
approach are profound relations between crossing symmetry of particle physics
and Hawking-Unruh like thermal aspects (KMS property, entropy attached to
horizons) of quantum matter behind causal horizons, aspects which hitherto were
exclusively related with Killing horizons in curved spacetime rather than with
localization aspects in Minkowski space particle physics. The scope of this
modular framework is amazingly wide and ranges from providing a conceptual
basis for the d=1+1 bootstrap-formfactor program for factorizable d=1+1 models
to a decomposition theory of QFT's in terms of a finite collection of unitarily
equivalent chiral conformal theories placed a specified relative position
within a common Hilbert space (in d=1+1 a holographic relation and in higher
dimensions more like a scanning). The new framework gives a spacetime
interpretation to the Zamolodchikov-Faddeev algebra and explains its thermal
aspects.Comment: In this form it will appear in JPA Math Gen, 47 pages tcilate
- …