7,145 research outputs found
Geometric overconvergence of rational functions in unbounded domains
The basic aim of this paper is to study the phenomenon of overconvergence for rational functions converging geometrically on [0, + ∞)
A new approach of analyzing GRB light curves
We estimated the Txx quantiles of the cumulative GRB light curves using our
recalculated background. The basic information of the light curves was
extracted by multivariate statistical methods. The possible classes of the
light curves are also briefly discussed.Comment: 4 pages, 8 figure
On Renyi entropies characterizing the shape and the extension of the phase space representation of quantum wave functions in disordered systems
We discuss some properties of the generalized entropies, called Renyi
entropies and their application to the case of continuous distributions. In
particular it is shown that these measures of complexity can be divergent,
however, their differences are free from these divergences thus enabling them
to be good candidates for the description of the extension and the shape of
continuous distributions. We apply this formalism to the projection of wave
functions onto the coherent state basis, i.e. to the Husimi representation. We
also show how the localization properties of the Husimi distribution on average
can be reconstructed from its marginal distributions that are calculated in
position and momentum space in the case when the phase space has no structure,
i.e. no classical limit can be defined. Numerical simulations on a one
dimensional disordered system corroborate our expectations.Comment: 8 pages with 2 embedded eps figures, RevTex4, AmsMath included,
submitted to PR
Information Length and Localization in One Dimension
The scaling properties of the wave functions in finite samples of the one
dimensional Anderson model are analyzed. The states have been characterized
using a new form of the information or entropic length, and compared with
analytical results obtained by assuming an exponential envelope function. A
perfect agreement is obtained already for systems of -- sites over
a very wide range of disorder parameter . Implications for
higher dimensions are also presented.Comment: 11 pages (+3 Figures upon request), Plain TE
A Successful Programme to Help Hungarian Intellectuals Beyond the Border
Collegium Talentum, a support system for Hungarian talent beyond the border, has been operating since 2011 in the Carpathian Basin. The aim of the programme is to train young researchers to become scientifically well-grounded specialists by both national and European standards, to attract fresh blood to academic institutions, and to inspire them to convey national cultural values in addition to having a scientific career. The programme supports the progress of 90 young doctoral students, thus significantly contributing to mitigating the crisis caused by the lack of intellectuals beyond the borders. More than 300 intellectuals from all over the Carpathian Basin have been involved in the programme to date, and a successful network has been organized of professors and researchers committed to national values
Quantum chaos in one dimension?
In this work we investigate the inverse of the celebrated
Bohigas-Giannoni-Schmit conjecture. Using two inversion methods we compute a
one-dimensional potential whose lowest N eigenvalues obey random matrix
statistics. Our numerical results indicate that in the asymptotic limit,
N->infinity, the solution is nowhere differentiable and most probably nowhere
continuous. Thus such a counterexample does not exist.Comment: 7 pages, 10 figures, minor correction, references extende
Divergent estimation error in portfolio optimization and in linear regression
The problem of estimation error in portfolio optimization is discussed, in
the limit where the portfolio size N and the sample size T go to infinity such
that their ratio is fixed. The estimation error strongly depends on the ratio
N/T and diverges for a critical value of this parameter. This divergence is the
manifestation of an algorithmic phase transition, it is accompanied by a number
of critical phenomena, and displays universality. As the structure of a large
number of multidimensional regression and modelling problems is very similar to
portfolio optimization, the scope of the above observations extends far beyond
finance, and covers a large number of problems in operations research, machine
learning, bioinformatics, medical science, economics, and technology.Comment: 5 pages, 2 figures, Statphys 23 Conference Proceedin
Spectral Properties of the Chalker-Coddington Network
We numerically investigate the spectral statistics of pseudo-energies for the
unitary network operator U of the Chalker--Coddington network. The shape of the
level spacing distribution as well the scaling of its moments is compared to
known results for quantum Hall systems. We also discuss the influence of
multifractality on the tail of the spacing distribution.Comment: JPSJ-style, 7 pages, 4 Postscript figures, to be published in J.
Phys. Soc. Jp
Fluctuation of the Correlation Dimension and the Inverse Participation Number at the Anderson Transition
The distribution of the correlation dimension in a power law band random
matrix model having critical, i.e. multifractal, eigenstates is numerically
investigated. It is shown that their probability distribution function has a
fixed point as the system size is varied exactly at a value obtained from the
scaling properties of the typical value of the inverse participation number.
Therefore the state-to-state fluctuation of the correlation dimension is
tightly linked to the scaling properties of the joint probability distribution
of the eigenstates.Comment: 4 pages, 5 figure
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