5,310 research outputs found
Probability-Changing Cluster Algorithm: Study of Three-Dimensional Ising Model and Percolation Problem
We present a detailed description of the idea and procedure for the newly
proposed Monte Carlo algorithm of tuning the critical point automatically,
which is called the probability-changing cluster (PCC) algorithm [Y. Tomita and
Y. Okabe, Phys. Rev. Lett. {\bf 86} (2001) 572]. Using the PCC algorithm, we
investigate the three-dimensional Ising model and the bond percolation problem.
We employ a refined finite-size scaling analysis to make estimates of critical
point and exponents. With much less efforts, we obtain the results which are
consistent with the previous calculations. We argue several directions for the
application of the PCC algorithm.Comment: 6 pages including 8 eps figures, to appear in J. Phys. Soc. Jp
Long wavelength iteration of Einstein's equations near a spacetime singularity
We clarify the links between a recently developped long wavelength iteration
scheme of Einstein's equations, the Belinski Khalatnikov Lifchitz (BKL) general
solution near a singularity and the antinewtonian scheme of Tomita's. We
determine the regimes when the long wavelength or antinewtonian scheme is
directly applicable and show how it can otherwise be implemented to yield the
BKL oscillatory approach to a spacetime singularity. When directly applicable
we obtain the generic solution of the scheme at first iteration (third order in
the gradients) for matter a perfect fluid. Specializing to spherical symmetry
for simplicity and to clarify gauge issues, we then show how the metric behaves
near a singularity when gradient effects are taken into account.Comment: 35 pages, revtex, no figure
Renormalization Group Approach to Einstein Equation in Cosmology
The renormalization group method has been adapted to the analysis of the
long-time behavior of non-linear partial differential equation and has
demonstrated its power in the study of critical phenomena of gravitational
collapse. In the present work we apply the renormalization group to the
Einstein equation in cosmology and carry out detailed analysis of
renormalization group flow in the vicinity of the scale invariant fixed point
in the spherically symmetric and inhomogeneous dust filled universe model.Comment: 16 pages including 2 eps figures, RevTe
Iterative Approach to Gravitational Lensing Theory
We develop an iterative approach to gravitational lensing theory based on
approximate solutions of the null geodesic equations. The approach can be
employed in any space-time which is ``close'' to a space-time in which the null
geodesic equations can be completely integrated, such as Minkowski space-time,
Robertson-Walker cosmologies, or Schwarzschild-Kerr geometries. To illustrate
the method, we construct the iterative gravitational lens equations and time of
arrival equation for a single Schwarzschild lens. This example motivates a
discussion of the relationship between the iterative approach, the standard
thin lens formulation, and an exact formulation of gravitational lensing.Comment: 27 pages, 2 figures, submitted to Phys.Rev.D, minor revisions, new
reference
Inhomogeneity of Spatial Curvature for Inflation
We study how the initial inhomogeneities of the spatial curvature affect the
onset of inflation in the closed universe. We consider a cosmological model
which contains a radiation and a cosmological constant. In order to treat the
inhomogeneities in the closed universe, we improve the long wavelength
approximation such that the non-small spatial curvature is tractable in the
lowest order. Using the improved scheme, we show how large inhomogeneities of
the spatial curvature prevent the occurrence of inflation.Comment: 17 pages, revtex, 6 figures included using eps
Monte Carlo analysis of critical phenomenon of the Ising model on memory stabilizer structures
We calculate the critical temperature of the Ising model on a set of graphs
representing a concatenated three-bit error-correction code. The graphs are
derived from the stabilizer formalism used in quantum error correction. The
stabilizer for a subspace is defined as the group of Pauli operators whose
eigenvalues are +1 on the subspace. The group can be generated by a subset of
operators in the stabilizer, and the choice of generators determines the
structure of the graph. The Wolff algorithm, together with the histogram method
and finite-size scaling, is used to calculate both the critical temperature and
the critical exponents of each structure. The simulations show that the choice
of stabilizer generators, both the number and the geometry, has a large effect
on the critical temperature.Comment: 7 pages, 6 figures, 5 table
General theory for decoy-state quantum key distribution with arbitrary number of intensities
We develop a general theory for quantum key distribution (QKD) in both the
forward error correction and the reverse error correction cases when the QKD
system is equipped with phase-randomized coherent light with arbitrary number
of decoy intensities. For this purpose, generalizing Wang's expansion, we
derive a convex expansion of the phase-randomized coherent state. We also
numerically check that the asymptotic key generation rates are almost saturated
when the number of decoy intensities is three.Comment: This manuscript has been revised extensivel
Spatial averaging and apparent acceleration in inhomogeneous spaces
As an alternative to dark energy that explains the observed acceleration of
the universe, it has been suggested that we may be at the center of an
inhomogeneous isotropic universe described by a Lemaitre-Tolman-Bondi (LTB)
solution of Einstein's field equations. To test this possibility, it is
necessary to solve the null geodesics. In this paper we first give a detailed
derivation of a fully analytical set of differential equations for the radial
null geodesics as functions of the redshift in LTB models. As an application we
use these equaions to show that a positive averaged acceleration obtained
in LTB models through spatial averaging can be incompatible with cosmological
observations. We provide examples of LTB models with positive which fail
to reproduce the observed luminosity distance . Since the apparent
cosmic acceleration is obtained from fitting the observed luminosity
distance to a FLRW model we conclude that in general a positive in LTB
models does not imply a positive .Comment: 16 pages, 12 figures. Explicit derivation of the fully analytical
null geodesic equations has been added. Published in GR
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