913 research outputs found
Phase transitions in spinor quantum gravity on a lattice
We construct a well-defined lattice-regularized quantum theory formulated in
terms of fundamental fermion and gauge fields, the same type of degrees of
freedom as in the Standard Model. The theory is explicitly invariant under
local Lorentz transformations and, in the continuum limit, under
diffeomorphisms. It is suitable for describing large nonperturbative and
fast-varying fluctuations of metrics. Although the quantum curved space turns
out to be on the average flat and smooth owing to the non-compressibility of
the fundamental fermions, the low-energy Einstein limit is not automatic: one
needs to ensure that composite metrics fluctuations propagate to long distances
as compared to the lattice spacing. One way to guarantee this is to stay at a
phase transition.
We develop a lattice mean field method and find that the theory typically has
several phases in the space of the dimensionless coupling constants, separated
by the second order phase transition surface. For example, there is a phase
with a spontaneous breaking of chiral symmetry. The effective low-energy
Lagrangian for the ensuing Goldstone field is explicitly
diffeomorphism-invariant. We expect that the Einstein gravitation is achieved
at the phase transition. A bonus is that the cosmological constant is probably
automatically zero.Comment: 37 pages, 12 figures Discussion of dimensions and of the
Berezinsky--Kosterlitz--Thouless phase adde
Position space versions of Magueijo-Smolin doubly special relativity proposal and the problem of total momentum
We present and discuss two different possibilities to construct position
space version for Magueijo-Smolin (MS) doubly special relativity proposal. The
first possibility is to start from ordinary special relativity and then to
define conserved momentum in special way. It generates MS invariant as well as
nonlinear MS transformations on the momentum space, leading to consistent
picture for one-particle sector of the theory. The second possibility is based
on the following observation. Besides the nonlinear MS transformations, the MS
energy-momentum relation is invariant also under some inhomogeneous linear
transformations. The latter are induced starting from linearly realized Lorentz
group in five-dimensional position space. Particle dynamics and kinematics are
formulated starting from the corresponding five-dimensional interval. There is
no problem of total momentum in the theory. The formulation admits two observer
independent scales, the speed of light, , and with dimension of
velocity. We speculate on different possibilities to relate with
fundamental constants. In particular, expression of in terms of vacuum
energy suggests emergence of (minimum) quantum of mass.Comment: Latex twice, 14 pages, revised in accordance with the version
publishedin Phys. Rev.
Space-time in light of Karolyhazy uncertainty relation
General relativity and quantum mechanics provide a natural explanation for
the existence of dark energy with its observed value and predict its dynamics.
Dark energy proves to be necessary for the existence of space-time itself and
determines the rate of its stability.Comment: 5 pages, Two misprints are correcte
Unimodular cosmology and the weight of energy
Some models are presented in which the strength of the gravitational coupling
of the potential energy relative to the same coupling for the kinetic energy
is, in a precise sense, adjustable. The gauge symmetry of these models consists
of those coordinate changes with unit jacobian.Comment: LaTeX, 23 pages, conclusions expanded. Two paragraphs and a new
reference adde
On the duality between the hyperbolic Sutherland and the rational Ruijsenaars-Schneider models
We consider two families of commuting Hamiltonians on the cotangent bundle of
the group GL(n,C), and show that upon an appropriate single symplectic
reduction they descend to the spectral invariants of the hyperbolic Sutherland
and of the rational Ruijsenaars-Schneider Lax matrices, respectively. The
duality symplectomorphism between these two integrable models, that was
constructed by Ruijsenaars using direct methods, can be then interpreted
geometrically simply as a gauge transformation connecting two cross sections of
the orbits of the reduction group.Comment: 16 pages, v2: comments and references added at the end of the tex
Apoastron Shift Constraints on Dark Matter Distribution at the Galactic Center
The existence of dark matter (DM) at scales of few pc down to pc around the centers of galaxies and in particular in the Galactic
Center region has been considered in the literature. Under the assumption that
such a DM clump, principally constituted by non-baryonic matter (like WIMPs)
does exist at the center of our galaxy, the study of the -ray emission
from the Galactic Center region allows us to constrain both the mass and the
size of this DM sphere. Further constraints on the DM distribution parameters
may be derived by observations of bright infrared stars around the Galactic
Center. Hall and Gondolo \cite{hallgondolo} used estimates of the enclosed mass
obtained in various ways and tabulated by Ghez et al.
\cite{Ghez_2003,Ghez_2005}. Moreover, if a DM cusp does exist around the
Galactic Center it could modify the trajectories of stars moving around it in a
sensible way depending on the DM mass distribution. Here, we discuss the
constraints that can be obtained with the orbit analysis of stars (as S2 and
S16) moving inside the DM concentration with present and next generations of
large telescopes. In particular, consideration of the S2 star apoastron shift
may allow improving limits on the DM mass and size.Comment: in press on Phys. Rev.
Black hole puncture initial data with realistic gravitational wave content
We present improved post-Newtonian-inspired initial data for non-spinning
black-hole binaries, suitable for numerical evolution with punctures. We
revisit the work of Tichy et al. [W. Tichy, B. Bruegmann, M. Campanelli, and P.
Diener, Phys. Rev. D 67, 064008 (2003)], explicitly calculating the remaining
integral terms. These terms improve accuracy in the far zone and, for the first
time, include realistic gravitational waves in the initial data. We investigate
the behavior of these data both at the center of mass and in the far zone,
demonstrating agreement of the transverse-traceless parts of the new metric
with quadrupole-approximation waveforms. These data can be used for numerical
evolutions, enabling a direct connection between the merger waveforms and the
post-Newtonian inspiral waveforms.Comment: 13 pages, 7 figures; replaced with published versio
Exact Evolution Operator on Non-compact Group Manifolds
Free quantal motion on group manifolds is considered. The Hamiltonian is
given by the Laplace -- Beltrami operator on the group manifold, and the
purpose is to get the (Feynman's) evolution kernel. The spectral expansion,
which produced a series of the representation characters for the evolution
kernel in the compact case, does not exist for non-compact group, where the
spectrum is not bounded. In this work real analytical groups are investigated,
some of which are of interest for physics. An integral representation for the
evolution operator is obtained in terms of the Green function, i.e. the
solution to the Helmholz equation on the group manifold. The alternative series
expressions for the evolution operator are reconstructed from the same integral
representation, the spectral expansion (when exists) and the sum over classical
paths. For non-compact groups, the latter can be interpreted as the (exact)
semi-classical approximation, like in the compact case. The explicit form of
the evolution operator is obtained for a number of non-compact groups.Comment: 32 pages, 5 postscript figures, LaTe
Pseudospectral Calculation of the Wavefunction of Helium and the Negative Hydrogen Ion
We study the numerical solution of the non-relativistic Schr\"{o}dinger
equation for two-electron atoms in ground and excited S-states using
pseudospectral (PS) methods of calculation. The calculation achieves
convergence rates for the energy, Cauchy error in the wavefunction, and
variance in local energy that are exponentially fast for all practical
purposes. The method requires three separate subdomains to handle the
wavefunction's cusp-like behavior near the two-particle coalescences. The use
of three subdomains is essential to maintaining exponential convergence. A
comparison of several different treatments of the cusps and the semi-infinite
domain suggest that the simplest prescription is sufficient. For many purposes
it proves unnecessary to handle the logarithmic behavior near the
three-particle coalescence in a special way. The PS method has many virtues: no
explicit assumptions need be made about the asymptotic behavior of the
wavefunction near cusps or at large distances, the local energy is exactly
equal to the calculated global energy at all collocation points, local errors
go down everywhere with increasing resolution, the effective basis using
Chebyshev polynomials is complete and simple, and the method is easily
extensible to other bound states. This study serves as a proof-of-principle of
the method for more general two- and possibly three-electron applications.Comment: 23 pages, 20 figures, 2 tables, Final refereed version - Some
references added, some stylistic changes, added paragraph to matrix methods
section, added last sentence to abstract
Biodiversity and species-environment relationships of the demersal fish assemblage at the Great Meteor Seamount (subtropical NE Atlantic), sampled by different trawls
Quantitative data collected with different bottom trawls at the Great Meteor Seamount (subtropical NE Atlantic, 30°N; 28.5°W) in 1967, 1970 and 1998 are compared. Bootstrap estimates of total catch per unit effort increased from 6.96 and 10.8 ind. m–1 h–1 in 1967 and 1970, respectively, to 583.98 ind. m–1 h–1 in 1998. Gear effects and an effect of gear over time accounted for 47.1% and 20% of species variability. Further significant factors were time of day and habitat, while season was not significant. A total of 43 species was collected. Including supplementary species information, a grand total of 46 species was found associated with the Great Meteor Seamount. Diversity was higher in 1967 and 1970 (Shannon's diversity: H′=2.5 and 1.6) than in 1998 (H′=0.9). Species–environment relationships are discussed in terms of a sound-scattering layer–interception hypothesis, i.e. utilisation of prey from a diurnally moving sound-scattering layer for the bentho-pelagic community. This is probably augmented by concentration effects in a circular current around the seamount (Taylor-column). Long-term changes are discussed with respect to a decrease in biodiversity due to considerable increases in Macroramphosus scolopax and Capros aper. In 1998, the increase of abundance of Trachurus picturatus and the respective decreases for genuine benthic species were likely to have been caused by a change of gear
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