34,702 research outputs found
Gravitational Theory with a Dynamical Time
A gravitational theory involving a vector field , whose zero
component has the properties of a dynamical time, is studied. The variation of
the action with respect to gives the covariant conservation of an
energy momentum tensor . Studying the theory in a
background which has killing vectors and killing tensors we find appropriate
shift symmetries of the field which lead to conservation laws. The
energy momentum that is the source of gravity is different
but related to and the covariant conservation of determines in general the vector field . When is chosen to be proportional to the metric, the theory
coincides with the Two Measures Theory, which has been studied before in
relation to the Cosmological Constant Problem. When the matter model consists
of point particles, or strings, the form of , solutions for
are found. For the case of a string gas cosmology, we find that
the Milne Universe can be a solution, where the gas of strings does not curve
the spacetime since although , , as a model for the early universe, this solution is also free
of the horizon problem. There may be also an application to the "time problem"
of quantum cosmology.Comment: 21 pages, discussions extended, some more explicit proofs included,
more references include
Phase diagrams of XXZ model on depleted square lattice
Using quantum Monte Carlo (QMC) simulations and a mean field (MF) theory, we
investigate the spin-1/2 XXZ model with nearest neighbor interactions on a
periodic depleted square lattice. In particular, we present results for 1/4
depleted lattice in an applied magnetic field and investigate the effect of
depletion on the ground state. The ground state phase diagram is found to
include an antiferromagnetic (AF) phase of magnetization and an
in-plane ferromagnetic (FM) phase with finite spin stiffness. The agreement
between the QMC simulations and the mean field theory based on resonating
trimers suggests the AF phase and in-plane FM phase can be interpreted as a
Mott insulator and superfluid of trimer states respectively. While the thermal
transitions of the in-plane FM phase are well described by the
Kosterlitz-Thouless transition, the quantum phase transition from the AF phase
to in-plane FM phase undergo a direct second order insulator-superfluid
transition upon increasing magnetic field.Comment: 7 pages, 8 figures. Revised version, accepted by PRB
Selected topics in Planck-scale physics
We review a few topics in Planck-scale physics, with emphasis on possible
manifestations in relatively low energy. The selected topics include quantum
fluctuations of spacetime, their cumulative effects, uncertainties in
energy-momentum measurements, and low energy quantum-gravity phenomenology. The
focus is on quantum-gravity-induced uncertainties in some observable
quantities. We consider four possible ways to probe Planck-scale physics
experimentally: 1. looking for energy-dependent spreads in the arrival time of
photons of the same energy from GRBs; 2. examining spacetime
fluctuation-induced phase incoherence of light from extragalactic sources; 3.
detecting spacetime foam with laser-based interferometry techniques; 4.
understanding the threshold anomalies in high energy cosmic ray and gamma ray
events. Some other experiments are briefly discussed. We show how some physics
behind black holes, simple clocks, simple computers, and the holographic
principle is related to Planck-scale physics. We also discuss a formulation of
the Dirac equation as a difference equation on a discrete Planck-scale
spacetime lattice, and a possible interplay between Planck-scale and
Hubble-scale physics encoded in the cosmological constant (dark energy).Comment: 31 pages, 1 figure; minor changes; to appear in Mod. Phys. Lett. A as
a Brief Revie
Probing the Galaxy I. The galactic structure towards the galactic pole
Observations of (B-V) colour distributions towards the galactic poles are
compared with those obtained from synthetic colour-magnitude diagrams to
determine the major constituents in the disc and spheroid. The disc is
described with four stellar sub-populations: the young, intermediate, old, and
thick disc populations, which have respectively scale heights of 100 pc, 250
pc, 0.5 kpc, and 1.0 kpc. The spheroid is described with stellar contributions
from the bulge and halo. The bulge is not well constrained with the data
analyzed in this study. A non-flattened power-law describes the observed
distributions at fainter magnitudes better than a deprojected R^{1/4}-law.
Details about the age, metallicity, and normalizations are listed in Table 1.
The star counts and the colour distributions from the stars in the intermediate
fields towards the galactic anti-centre are well described with the stellar
populations mentioned above. Arguments are given that the actual solar offset
is about 15 pc north from the galactic plane.Comment: 11 pages TeX, 4 separate pages with additional figures, accepted for
publication in A&
Testing Cluster Structure of Graphs
We study the problem of recognizing the cluster structure of a graph in the
framework of property testing in the bounded degree model. Given a parameter
, a -bounded degree graph is defined to be -clusterable, if it can be partitioned into no more than parts, such
that the (inner) conductance of the induced subgraph on each part is at least
and the (outer) conductance of each part is at most
, where depends only on . Our main
result is a sublinear algorithm with the running time
that takes as
input a graph with maximum degree bounded by , parameters , ,
, and with probability at least , accepts the graph if it
is -clusterable and rejects the graph if it is -far from
-clusterable for , where depends only on . By the lower
bound of on the number of queries needed for testing graph
expansion, which corresponds to in our problem, our algorithm is
asymptotically optimal up to polylogarithmic factors.Comment: Full version of STOC 201
Macroeconomics modelling on UK GDP growth by neural computing
This paper presents multilayer neural networks used in UK gross domestic product estimation. These networks are trained by backpropagation and genetic algorithm based methods. Different from backpropagation guided by gradients of the performance, the genetic algorithm directly evaluates the performance of multiple sets of neural networks in parallel and then uses the analysed results to breed new networks that tend to be better suited to the problems in hand. It is shown that this guided evolution leads to globally optimal networks and more accurate results, with less adjustment of the algorithm needed
The fluctuation spectra around a Gaussian classical solution of a tensor model and the general relativity
Tensor models can be interpreted as theory of dynamical fuzzy spaces. In this
paper, I study numerically the fluctuation spectra around a Gaussian classical
solution of a tensor model, which represents a fuzzy flat space in arbitrary
dimensions. It is found that the momentum distribution of the low-lying
low-momentum spectra is in agreement with that of the metric tensor modulo the
general coordinate transformation in the general relativity at least in the
dimensions studied numerically, i.e. one to four dimensions. This result
suggests that the effective field theory around the solution is described in a
similar manner as the general relativity.Comment: 29 pages, 13 figure
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