21,860 research outputs found
Geometry of escort distributions
Given an original distribution, its statistical and probabilistic attributs
may be scanned by the associated escort distribution introduced by Beck and
Schlogl and employed in the formulation of nonextensive statistical mechanics.
Here, the geometric structure of the one-parameter family of the escort
distributions is studied based on the Kullback-Leibler divergence and the
relevant Fisher metric. It is shown that the Fisher metric is given in terms of
the generalized bit-variance, which measures fluctuations of the crowding index
of a multifractal. The Cramer-Rao inequality leads to the fundamental limit for
precision of statistical estimate of the order of the escort distribution. It
is also quantitatively discussed how inappropriate it is to use the original
distribution instead of the escort distribution for calculating the expectation
values of physical quantities in nonextensive statistical mechanics.Comment: 12 pages, no figure
Stability of Tsallis antropy and instabilities of Renyi and normalized Tsallis entropies: A basis for q-exponential distributions
The q-exponential distributions, which are generalizations of the
Zipf-Mandelbrot power-law distribution, are frequently encountered in complex
systems at their stationary states. From the viewpoint of the principle of
maximum entropy, they can apparently be derived from three different
generalized entropies: the Renyi entropy, the Tsallis entropy, and the
normalized Tsallis entropy. Accordingly, mere fittings of observed data by the
q-exponential distributions do not lead to identification of the correct
physical entropy. Here, stabilities of these entropies, i.e., their behaviors
under arbitrary small deformation of a distribution, are examined. It is shown
that, among the three, the Tsallis entropy is stable and can provide an
entropic basis for the q-exponential distributions, whereas the others are
unstable and cannot represent any experimentally observable quantities.Comment: 20 pages, no figures, the disappeared "primes" on the distributions
are added. Also, Eq. (65) is correcte
U-Spin Tests of the Standard Model and New Physics
Within the standard model, a relation involving branching ratios and direct
CP asymmetries holds for the B-decay pairs that are related by U-spin. The
violation of this relation indicates new physics (NP). In this paper, we assume
that the NP affects only the Delta S = 1 decays, and show that the NP operators
are generally the same as those appearing in B -> pi K decays. The fit to the
latest B -> pi K data shows that only one NP operator is sizeable. As a
consequence, the relation is expected to be violated for only one decay pair:
Bd -> K0 pi0 and Bs -> Kbar0 pi0.Comment: 12 pages, latex, no figures. References changed to follow MPL
guidelines; info added about U-spin breaking and small NP strong phases;
discussion added about final-state pi-K rescattering; analysis and
conclusions unaltere
Microcanonical Foundation for Systems with Power-Law Distributions
Starting from microcanonical basis with the principle of equal a priori
probability, it is found that, besides ordinary Boltzmann-Gibbs theory with the
exponential distribution, a theory describing systems with power-law
distributions can also be derived.Comment: 9 page
Inverse kinetic theory for incompressible thermofluids
An interesting issue in fluid dynamics is represented by the possible
existence of inverse kinetic theories (IKT) which are able to deliver, in a
suitable sense, the complete set of fluid equations which are associated to a
prescribed fluid. From the mathematical viewpoint this involves the formal
description of a fluid by means of a classical dynamical system which advances
in time the relevant fluid fields. The possibility of defining an IKT for the
3D incompressible Navier-Stokes equations (INSE), recently investigated (Ellero
\textit{et al}, 2004-2007) raises the interesting question whether the theory
can be applied also to thermofluids, in such a way to satisfy also the second
principle of thermodynamics. The goal of this paper is to prove that such a
generalization is actually possible, by means of a suitable \textit{extended
phase-space formulation}. We consider, as a reference test, the case of
non-isentropic incompressible thermofluids, whose dynamics is described by the
Fourier and the incompressible Navier-Stokes equations, the latter subject to
the conditions of validity of the Boussinesq approximation.Comment: Contributed paper at RGD26 (Kyoto, Japan, July 2008
Scherk-Schwarz SUSY breaking from the viewpoint of 5D conformal supergravity
We reinterpret the Scherk-Schwarz (SS) boundary condition for SU(2)_R in a
compactified five-dimensional (5D) Poincare supergravity in terms of the
twisted SU(2)_U gauge fixing in 5D conformal supergravity. In such translation,
only the compensator hypermultiplet is relevant to the SS twist, and various
properties of the SS mechanism can be easily understood. Especially, we show
the correspondence between the SS twist and constant superpotentials within our
framework.Comment: 16 pages, no figur
The Rare Top Decays and
The large value of the top quark mass implies that the rare top decays and , and and
, are kinematically allowed decays so long as or , respectively. The partial decay widths for these decay modes
are calculated in the standard model. The partial widths depend sensitively on
the precise value of the top quark mass. The branching ratio for is as much as for , and could be
observable at LHC. The rare decay modes and are highly GIM-suppressed, and thus provide a means for testing the GIM
mechanism for three generations of quarks in the u, c, t sector.Comment: 19 pages, latex, t->bWZ corrected, previous literature on t->bWZ
cited, t->cWW unchange
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