4,473 research outputs found
Infinitely Many Stochastically Stable Attractors
Let f be a diffeomorphism of a compact finite dimensional boundaryless
manifold M exhibiting infinitely many coexisting attractors. Assume that each
attractor supports a stochastically stable probability measure and that the
union of the basins of attraction of each attractor covers Lebesgue almost all
points of M. We prove that the time averages of almost all orbits under random
perturbations are given by a finite number of probability measures. Moreover
these probability measures are close to the probability measures supported by
the attractors when the perturbations are close to the original map f.Comment: 14 pages, 2 figure
Mass-Temperature Relation of Galaxy Clusters: A Theoretical Study
Combining conservation of energy throughout nearly-spherical collapse of
galaxy clusters with the virial theorem, we derive the mass-temperature
relation for X-ray clusters of galaxies . The normalization factor
and the scatter of the relation are determined from first principles with
the additional assumption of initial Gaussian random field. We are also able to
reproduce the recently observed break in the M-T relation at T \sim 3 \keV,
based on the scatter in the underlying density field for a low density
CDM cosmology. Finally, by combining observational data of high
redshift clusters with our theoretical formalism, we find a semi-empirical
temperature-mass relation which is expected to hold at redshifts up to unity
with less than 20% error.Comment: 43 pages, 13 figures, One figure is added and minor changes are made.
Accepted for Publication in Ap
The evolution of clustering and bias in the galaxy distribution
This paper reviews the measurements of galaxy correlations at high redshifts,
and discusses how these may be understood in models of hierarchical
gravitational collapse. The clustering of galaxies at redshift one is much
weaker than at present, and this is consistent with the rate of growth of
structure expected in an open universe. If , this observation would
imply that bias increases at high redshift, in conflict with observed
values for known high- clusters. At redshift 3, the population of
Lyman-limit galaxies displays clustering which is of similar amplitude to that
seen today. This is most naturally understood if the Lyman-limit population is
a set of rare recently-formed objects. Knowing both the clustering and the
abundance of these objects, it is possible to deduce empirically the
fluctuation spectrum required on scales which cannot be measured today owing to
gravitational nonlinearities. Of existing physical models for the fluctuation
spectrum, the results are most closely matched by a low-density spatially flat
universe. This conclusion is reinforced by an empirical analysis of CMB
anisotropies, in which the present-day fluctuation spectrum is forced to have
the observed form. Open models are strongly disfavoured, leaving CDM
as the most successful simple model for structure formation.Comment: Invited review at the Royal Society Meeting `Large-scale structure in
the universe', London, March 1998. 20 Pages LaTe
Normalization procedure for relaxation studies in NMR quantum information processing
NMR quantum information processing studies rely on the reconstruction of the
density matrix representing the so-called pseudo-pure states (PPS). An
initially pure part of a PPS state undergoes unitary and non-unitary
(relaxation) transformations during a computation process, causing a "loss of
purity" until the equilibrium is reached. Besides, upon relaxation, the nuclear
polarization varies in time, a fact which must be taken into account when
comparing density matrices at different instants. Attempting to use time-fixed
normalization procedures when relaxation is present, leads to various anomalies
on matrices populations. On this paper we propose a method which takes into
account the time-dependence of the normalization factor. From a generic form
for the deviation density matrix an expression for the relaxing initial pure
state is deduced. The method is exemplified with an experiment of relaxation of
the concurrence of a pseudo-entangled state, which exhibits the phenomenon of
sudden death, and the relaxation of the Wigner function of a pseudo-cat state.Comment: 9 pages, 5 figures, to appear in QI
Weak Lensing as a Calibrator of the Cluster Mass-Temperature Relation
The abundance of clusters at the present epoch and weak gravitational lensing
shear both constrain roughly the same combination of the power spectrum
normalization sigma_8 and matter energy density Omega_M. The cluster constraint
further depends on the normalization of the mass-temperature relation.
Therefore, combining the weak lensing and cluster abundance data can be used to
accurately calibrate the mass-temperature relation. We discuss this approach
and illustrate it using data from recent surveys.Comment: Matches the version in ApJL. Equation 4 corrected. Improvements in
the analysis move the cluster contours in Fig1 slightly upwards. No changes
in the conclusion
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