339 research outputs found
Collective Origin of the Coexistence of Apparent RMT Noise and Factors in Large Sample Correlation Matrices
Through simple analytical calculations and numerical simulations, we
demonstrate the generic existence of a self-organized macroscopic state in any
large multivariate system possessing non-vanishing average correlations between
a finite fraction of all pairs of elements. The coexistence of an eigenvalue
spectrum predicted by random matrix theory (RMT) and a few very large
eigenvalues in large empirical correlation matrices is shown to result from a
bottom-up collective effect of the underlying time series rather than a
top-down impact of factors. Our results, in excellent agreement with previous
results obtained on large financial correlation matrices, show that there is
relevant information also in the bulk of the eigenvalue spectrum and
rationalize the presence of market factors previously introduced in an ad hoc
manner.Comment: 4 pages with 3 figur
Signatures of the disk-jet coupling in the Broad-line Radio Quasar 4C+74.26
Here we explore the disk-jet connection in the broad-line radio quasar
4C+74.26, utilizing the results of the multiwavelength monitoring of the
source. The target is unique in that its radiative output at radio wavelengths
is dominated by a moderately-beamed nuclear jet, at optical frequencies by the
accretion disk, and in the hard X-ray range by the disk corona. Our analysis
reveals a correlation (local and global significance of 96\% and 98\%,
respectively) between the optical and radio bands, with the disk lagging behind
the jet by days. We discuss the possible explanation for this,
speculating that the observed disk and the jet flux changes are generated by
magnetic fluctuations originating within the innermost parts of a truncated
disk, and that the lag is related to a delayed radiative response of the disk
when compared with the propagation timescale of magnetic perturbations along
relativistic outflow. This scenario is supported by the re-analysis of the
NuSTAR data, modelled in terms of a relativistic reflection from the disk
illuminated by the coronal emission, which returns the inner disk radius
. We discuss the global energetics in
the system, arguing that while the accretion proceeds at the Eddington rate,
with the accretion-related bolometric luminosity erg s , the jet total kinetic energy
erg s, inferred from the dynamical
modelling of the giant radio lobes in the source, constitutes only a small
fraction of the available accretion power.Comment: 9 pages and 6 figures, ApJ accepte
A Stable and Robust Calibration Scheme of the Log-Periodic Power Law Model
We present a simple transformation of the formulation of the log-periodic
power law formula of the Johansen-Ledoit-Sornette model of financial bubbles
that reduces it to a function of only three nonlinear parameters. The
transformation significantly decreases the complexity of the fitting procedure
and improves its stability tremendously because the modified cost function is
now characterized by good smooth properties with in general a single minimum in
the case where the model is appropriate to the empirical data. We complement
the approach with an additional subordination procedure that slaves two of the
nonlinear parameters to what can be considered to be the most crucial nonlinear
parameter, the critical time defined as the end of the bubble and the
most probably time for a crash to occur. This further decreases the complexity
of the search and provides an intuitive representation of the results of the
calibration. With our proposed methodology, metaheuristic searches are not
longer necessary and one can resort solely to rigorous controlled local search
algorithms, leading to dramatic increase in efficiency. Empirical tests on the
Shanghai Composite index (SSE) from January 2007 to March 2008 illustrate our
findings
Many-body Systems Interacting via a Two-body Random Ensemble (I): Angular Momentum distribution in the ground states
In this paper, we discuss the angular momentum distribution in the ground
states of many-body systems interacting via a two-body random ensemble.
Beginning with a few simple examples, a simple approach to predict P(I)'s,
angular momenta I ground state (g.s.) probabilities, of a few solvable cases,
such as fermions in a small single-j shell and d boson systems, is given. This
method is generalized to predict P(I)'s of more complicated cases, such as even
or odd number of fermions in a large single-j shell or a many-j shell, d-boson,
sd-boson or sdg-boson systems, etc. By this method we are able to tell which
interactions are essential to produce a sizable P(I) in a many-body system. The
g.s. probability of maximum angular momentum is discussed. An
argument on the microscopic foundation of our approach, and certain matrix
elements which are useful to understand the observed regularities, are also
given or addressed in detail. The low seniority chain of 0 g.s. by using the
same set of two-body interactions is confirmed but it is noted that
contribution to the total 0 g.s. probability beyond this chain may be more
important for even fermions in a single-j shell. Preliminary results by taking
a displaced two-body random ensemble are presented for the I g.s.
probabilities.Comment: 39 pages and 8 figure
Density-matrix formalism with three-body ground-state correlations
A density-matrix formalism which includes the effects of three-body ground-
state correlations is applied to the standard Lipkin model. The reason to
consider the complicated three-body correlations is that the truncation scheme
of reduced density matrices up to the two-body level does not give satisfactory
results to the standard Lipkin model. It is shown that inclusion of the
three-body correlations drastically improves the properties of the ground
states and excited states. It is pointed out that lack of mean-field effects in
the standard Lipkin model enhances the relative importance of the three-body
ground-state correlations. Formal aspects of the density-matrix formalism such
as a relation to the variational principle and the stability condition of the
ground state are also discussed. It is pointed out that the three-body
ground-state correlations are necessary to satisfy the stability condition
Convergence of the critical attractor of dissipative maps: Log-periodic oscillations, fractality and nonextensivity
For a family of logistic-like maps, we investigate the rate of convergence to
the critical attractor when an ensemble of initial conditions is uniformly
spread over the entire phase space. We found that the phase space volume
occupied by the ensemble W(t) depicts a power-law decay with log-periodic
oscillations reflecting the multifractal character of the critical attractor.
We explore the parametric dependence of the power-law exponent and the
amplitude of the log-periodic oscillations with the attractor's fractal
dimension governed by the inflexion of the map near its extremal point.
Further, we investigate the temporal evolution of W(t) for the circle map whose
critical attractor is dense. In this case, we found W(t) to exhibit a rich
pattern with a slow logarithmic decay of the lower bounds. These results are
discussed in the context of nonextensive Tsallis entropies.Comment: 8 pages and 8 fig
Precursor flares in OJ 287
We have studied three most recent precursor flares in the light curve of the
blazar OJ 287 while invoking the presence of a precessing binary black hole in
the system to explain the nature of these flares. Precursor flare timings from
the historical light curves are compared with theoretical predictions from our
model that incorporate effects of an accretion disk and post-Newtonian
description for the binary black hole orbit. We find that the precursor flares
coincide with the secondary black hole descending towards the accretion disk of
the primary black hole from the observed side, with a mean z-component of
approximately z_c = 4000 AU. We use this model of precursor flares to predict
that precursor flare of similar nature should happen around 2020.96 before the
next major outburst in 2022.Comment: to appear in the Astrophysical Journa
Generic Rotation in a Collective SD Nucleon-Pair Subspace
Low-lying collective states involving many nucleons interacting by a random
ensemble of two-body interactions (TBRE) are investigated in a collective
SD-pair subspace, with the collective pairs defined dynamically from the
two-nucleon system. It is found that in this truncated pair subspace collective
vibrations arise naturally for a general TBRE hamiltonian whereas collective
rotations do not. A hamiltonian restricted to include only a few randomly
generated separable terms is able to produce collective rotational behavior, as
long as it includes a reasonably strong quadrupole-quadrupole component.
Similar results arise in the full shell model space. These results suggest that
the structure of the hamiltonian is key to producing generic collective
rotation.Comment: 11 pages, 5 figure
Universal Predictions for Statistical Nuclear Correlations
We explore the behavior of collective nuclear excitations under a
multi-parameter deformation of the Hamiltonian. The Hamiltonian matrix elements
have the form , with a
parametric correlation of the type . The studies are done in both the regular and chaotic regimes of the
Hamiltonian. Model independent predictions for a wide variety of correlation
functions and distributions which depend on wavefunctions and energies are
found from parametric random matrix theory and are compared to the nuclear
excitations. We find that our universal predictions are observed in the nuclear
states. Being a multi-parameter theory, we consider general paths in parameter
space and find that universality can be effected by the topology of the
parameter space. Specifically, Berry's phase can modify short distance
correlations, breaking certain universal predictions.Comment: Latex file + 12 postscript figure
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