19,511 research outputs found
A Degeneracy in DRW Modelling of AGN Light Curves
Individual light curves of active galactic nuclei (AGNs) are nowadays
successfully modelled with the damped random walk (DRW) stochastic process,
characterized by the power exponential covariance matrix of the signal, with
the power . By Monte Carlo simulation means, we generate mock AGN
light curves described by non-DRW stochastic processes (
and ) and show they can be successfully and well-modelled as a
single DRW process, obtaining comparable goodness of fits. A good DRW fit, in
fact, may not mean that DRW is the true underlying process leading to
variability and it cannot be used as a proof for it. When comparing the input
(non-DRW) and measured (DRW) process parameters, the recovered time scale
(amplitude) increases (decreases) with the increasing input . In
practice, this means that the recovered DRW parameters may lead to biased (or
even non-existing) correlations of the variability and physical parameters of
AGNs if the true AGN variability is caused by non-DRW stochastic processes. The
proper way of identifying the processes leading to variability are
model-independent structure functions and/or power spectral densities and then
using such information on the covariance matrix of the signal in light curve
modelling.Comment: 3 pages, 2 figures, accepted for publication in MNRAS, final versio
Opportunity for Regulating the Collective Effect of Random Expansion with Manifestations of Finite Size Effects in a Moderate Number of Finite Systems
One reports computational study revealing a set of general requirements,
fulfilling of which would allow employing changes in ambient conditions to
regulate accomplishing the collective outcome of emerging active network
patterns in an ensemble of a moderate number of finite discrete systems. The
patterns within all these component systems emerge out of random expansion
process governed by certain local rule. The systems modeled are of the same
type but different in details, finite discrete spatial domains of the expansion
within the systems are equivalent regular hexagonal arrays. The way in which
elements of a component system function in the local information transmission
allows dividing them into two classes. One class is represented by
zero-dimensional entities coupled into pairs identified at the array sites
being nearest neighbors. The pairs preserve their orientation in the space
while experiencing conditional hopping to positions close by and transferring
certain information portions. Messenger particles hopping to signal the pairs
for the conditional jumping constitute the other class. Contribution from the
hopping pairs results in finite size effects being specific feature of
accomplishing the mean expected network pattern representing the collective
outcome. It is shown how manifestations of the finite size effects allow using
changes in parameters of the model ambient conditions of the ensemble evolution
to regulate accomplishing the collective outcome representation.Comment: 22 pages, 10 eps figures, corrected URL address placing in text,
minor editorial correction in sec.2, author e-mail change
On condensation properties of Bethe roots associated with the XXZ chain
I prove that the Bethe roots describing either the ground state or a certain
class of "particle-hole" excited states of the XXZ spin- chain in any
sector with magnetisation exist and form, in the
infinite volume limit, a dense distribution on a subinterval of .
The results holds for any value of the anisotropy . In fact, I
establish an even stronger result, namely the existence of an all order
asymptotic expansion of the counting function associated with such roots. As a
corollary, these results allow one to prove the existence and form of the
infinite volume limit of various observables attached to the model -the
excitation energy, momentum, the zero temperature correlation functions, so as
to name a few- that were argued earlier in the literature.Comment: 54 pages, 2 figures. Some details in proof adde
On singularities of dynamic response functions in the massless regime of the XXZ spin-1/2 chain
This work extracts, by means of an exact analysis, the singular behaviour of
the dynamical response functions -- the Fourier transforms of dynamical
two-point functions -- in the vicinity of the various excitation thresholds in
the massless regime of the XXZ spin-1/2 chain. The analysis yields the edge
exponents and associated amplitudes which describe the local behaviour of the
response function near a threshold. The singular behaviour is derived starting
from first principle considerations: the method of analysis \textit{does not
rely, at any stage}, on some hypothetical correspondence with a field theory or
other phenomenological approaches. The analysis builds on the massless form
factor expansion for the response functions of the XXZ chain obtained recently
by the author.
It confirms the non-linear Luttinger based predictions relative to the
power-law behaviour and of the associated edge exponents which arise in the
vicinity of the dispersion relation of one massive excitation (hole, particle
or bound state). In addition, the present analysis shows that, due to the lack
of strict convexity of the particles dispersion relation and due to the
presence of slow velocity branches of the bound states, there exist excitation
thresholds with a different structure of edge exponents. These origin from
multi-particle/hole/bound state excitations maximising the energy at fixed
momentum.Comment: 115 pages, 6 figure
On the emptiness formation probability of the open XXZ spin-\tf{1}{2} chain
This paper is devoted to the study of the emptiness formation probability
\tau\pa{m} of the open XXZ chain. We derive a closed form for \tau\pa{m} at
\Delta=\tf{1}{2} when the boundary field vanishes. Moreover we obtain its
leading asymptotics for an arbitrary boundary field at the free fermion point.
Finally, we compute the first term of the asymptotics of \ln\pa{\tau\pa{m}}
in the whole massless regime .Comment: 18 page
On lacunary Toeplitz determinants
By using Riemann--Hilbert problem based techniques, we obtain the asymptotic
expansion of lacunary Toeplitz determinants generated by holomorhpic symbols, where (resp. )
except for a finite subset of indices (resp. ). In addition to the usual Szeg\"{o} asymptotics, our answer involves a
determinant of size .Comment: 11 page
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