12,270 research outputs found
Mode fluctuations as fingerprint of chaotic and non-chaotic systems
The mode-fluctuation distribution is studied for chaotic as well as
for non-chaotic quantum billiards. This statistic is discussed in the broader
framework of the functions being the probability of finding energy
levels in a randomly chosen interval of length , and the distribution of
, where is the number of levels in such an interval, and their
cumulants . It is demonstrated that the cumulants provide a possible
measure for the distinction between chaotic and non-chaotic systems. The
vanishing of the normalized cumulants , , implies a Gaussian
behaviour of , which is realized in the case of chaotic systems, whereas
non-chaotic systems display non-vanishing values for these cumulants leading to
a non-Gaussian behaviour of . For some integrable systems there exist
rigorous proofs of the non-Gaussian behaviour which are also discussed. Our
numerical results and the rigorous results for integrable systems suggest that
a clear fingerprint of chaotic systems is provided by a Gaussian distribution
of the mode-fluctuation distribution .Comment: 44 pages, Postscript. The figures are included in low resolution
only. A full version is available at
http://www.physik.uni-ulm.de/theo/qc/baecker.htm
Dynamic scaling and universality in evolution of fluctuating random networks
We found that models of evolving random networks exhibit dynamic scaling
similar to scaling of growing surfaces. It is demonstrated by numerical
simulations of two variants of the model in which nodes are added as well as
removed [Phys. Rev. Lett. 83, 5587 (1999)]. The averaged size and connectivity
of the network increase as power-laws in early times but later saturate.
Saturated values and times of saturation change with paramaters controlling the
local evolution of the network topology. Both saturated values and times of
saturation obey also power-law dependences on controlling parameters. Scaling
exponents are calculated and universal features are discussed.Comment: 7 pages, 6 figures, Europhysics Letters for
Testing the performance and accuracy of the RELXILL model for the relativistic X-ray reflection from accretion disks
The reflection spectroscopic model RELXILL is commonly implemented in
studying relativistic X-ray reflection from accretion disks around black holes.
We present a systematic study of the model's capability to constrain the
dimensionless spin and ionization parameters from 6,000 NuSTAR
simulations of a bright X-ray source employing the lamppost geometry. We employ
high count spectra to show the limitations in the model without being confused
with limitations in signal-to-noise. We find that both parameters are
well-recovered at 90% confidence with improving constraints at higher
reflection fraction, high spin, and low source height. We test spectra across a
broad range - first at 1010 and then 10 total source counts
across the effective 3-79 keV band of NuSTAR, and discover a strong dependence
of the results on how fits are performed around the starting parameters, owing
to the complexity of the model itself. A blind fit chosen over an approach that
carries some estimates of the actual parameter values can lead to significantly
worse recovery of model parameters. We further stress on the importance to span
the space of nonlinear-behaving parameters like carefully and
thoroughly for the model to avoid misleading results. In light of selecting
fitting procedures, we recall the necessity to pay attention to the choice of
data binning and fit statistics used to test the goodness of fit by
demonstrating the effect on the photon index . We re-emphasize and
implore the need to account for the detector resolution while binning X-ray
data and using Poisson fit statistics instead while analyzing Poissonian data.Comment: 9 pages, 6 figures, accepted for publication in Ap
Escape Orbits for Non-Compact Flat Billiards
It is proven that, under some conditions on , the non-compact flat
billiard
has no orbits going {\em directly} to . The relevance of such
sufficient conditions is discussed.Comment: 9 pages, LaTeX, 3 postscript figures available at
http://www.princeton.edu/~marco/papers/ . Minor changes since previously
posted version. Submitted to 'Chaos
The equation of state of neutron star matter and the symmetry energy
We present an overview of microscopical calculations of the Equation of State
(EOS) of neutron matter performed using Quantum Monte Carlo techniques. We
focus to the role of the model of the three-neutron force in the high-density
part of the EOS up to a few times the saturation density. We also discuss the
interplay between the symmetry energy and the neutron star mass-radius
relation.
The combination of theoretical models of the EOS with recent neutron stars
observations permits us to constrain the value of the symmetry energy and its
slope. We show that astrophysical observations are starting to provide
important insights into the properties of neutron star matter.Comment: 7 pages, 3 figure, talk given at the 11th International Conference on
Nucleus-Nucleus Collisions (NN2012), San Antonio, Texas, USA, May 27-June 1,
2012. To appear in the NN2012 Proceedings in Journal of Physics: Conference
Series (JPCS
X-ray Reflection Spectroscopy of the Black Hole GX 339-4: Exploring the Hard State with Unprecedented Sensitivity
We analyze {\it simultaneously} six composite {\it RXTE} spectra of GX 339--4
in the hard state comprising 77 million counts collected over 196 ks. The
source spectra are ordered by luminosity and spanthe range 1.6\% to 17\% of the
Eddington luminosity. Crucially, using our new tool {\tt pcacorr}, we
re-calibrate the data to a precision of 0.1\%, an order of magnitude
improvement over all earlier work. Using our advanced reflection model {\tt
relxill}, we target the strong features in the component of emission reflected
from the disk, namely, the relativistically-broadened Fe K emission line, the
Fe K edge and the Compton hump. We report results for two joint fits to the six
spectra: For the first fit, we fix the spin parameter to its maximal value
() and allow the inner disk radius to vary. Results
include (i) precise measurements of , with evidence that the disk
becomes slightly truncated at a few percent of Eddington; and (ii) an
order-of-magnitude swing with luminosity in the high energy cutoff, which
reaches keV at our lowest luminosity. For the second fit, we make the
standard assumption in estimating spin that the inner edge of the accretion
disk is located at the innermost stable circular orbit () and find (90\% confidence,
statistical). For both fits, and at the same level of statistical confidence,
we estimate that the disk inclination is deg and that the Fe
abundance is super-solar, .Comment: Accepted for publication in ApJ, 20 pages, 13 figure
Energy-dependent evolution in IC10 X-1: hard evidence for an extended corona and implications
We have analyzed a ~130 ks XMM-Newton observation of the dynamically confirmed black hole + Wolf-Rayet (BH+WR) X-ray binary (XB) IC10 X-1, covering ~1 orbital cycle. This system experiences periodic intensity dips every ~35 hr. We find that energy-independent evolution is rejected at a >5σ level. The spectral and timing evolution of IC10 X-1 are best explained by a compact disk blackbody and an extended Comptonized component, where the thermal component is completely absorbed and the Comptonized component is partially covered during the dip. We consider three possibilities for the absorber: cold material in the outer accretion disk, as is well documented for Galactic neutron star (NS) XBs at high inclination; a stream of stellar wind that is enhanced by traveling through the L1 point; and a spherical wind. We estimated the corona radius (r ADC) for IC10 X-1 from the dip ingress to be ~106 km, assuming absorption from the outer disk, and found it to be consistent with the relation between r ADC and 1-30 keV luminosity observed in Galactic NS XBs that spans two orders of magnitude. For the other two scenarios, the corona would be larger. Prior BH mass (M BH) estimates range over 23-38 M ☉, depending on the inclination and WR mass. For disk absorption, the inclination, i, is likely to be ~60-80°, with M BH ~ 24-41 M ☉. Alternatively, the L1-enhanced wind requires i ~ 80°, suggesting ~24-33 M ☉. For a spherical absorber, i ~ 40°, and M BH ~ 50-65 M ☉
Genralized Robustness of Entanglement
The robustness of entanglement results of Vidal and Tarrach considered the
problem whereby an entangled state is mixed with a separable state so that the
overall state becomes non-entangled. In general it is known that there are also
cases when entangled states are mixed with other entangled states and where the
sum is separable. In this paper, we treat the more general case where entangled
states can be mixed with any states so that the resulting mixture is
unentangled. It is found that entangled pure states for this generalized case
have the same robustness as the restricted case of Vidal and Tarrach.Comment: Final version. Editorial changes and references added to independent
wor
Categorification of persistent homology
We redevelop persistent homology (topological persistence) from a categorical
point of view. The main objects of study are diagrams, indexed by the poset of
real numbers, in some target category. The set of such diagrams has an
interleaving distance, which we show generalizes the previously-studied
bottleneck distance. To illustrate the utility of this approach, we greatly
generalize previous stability results for persistence, extended persistence,
and kernel, image and cokernel persistence. We give a natural construction of a
category of interleavings of these diagrams, and show that if the target
category is abelian, so is this category of interleavings.Comment: 27 pages, v3: minor changes, to appear in Discrete & Computational
Geometr
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