243 research outputs found
Hard rods: statistics of parking configurations
We compute the correlation function in the equilibrium version of R\'enyi's
{\sl parking problem}. The correlation length is found to diverge as
when (maximum density) and as
when (minimum density).Comment: 9 pages, 1 figur
Strong superadditivity and monogamy of the Renyi measure of entanglement
Employing the quantum R\'enyi -entropies as a measure of
entanglement, we numerically find the violation of the strong superadditivity
inequality for a system composed of four qubits and . This violation
gets smaller as and vanishes for when the
measure corresponds to the Entanglement of Formation (EoF). We show that the
R\'enyi measure aways satisfies the standard monogamy of entanglement for
, and only violates a high order monogamy inequality, in the rare
cases in which the strong superadditivity is also violated. The sates
numerically found where the violation occurs have special symmetries where both
inequalities are equivalent. We also show that every measure satisfing monogamy
for high dimensional systems also satisfies the strong superadditivity
inequality. For the case of R\'enyi measure, we provide strong numerical
evidences that these two properties are equivalent.Comment: replaced with final published versio
Thermostatistics based on Kolmogorov-Nagumo averages: Unifying framework for extensive and nonextensive generalizations
We show that extensive thermostatistics based on Renyi entropy and
Kolmogorov-Nagumo averages can be expressed in terms of Tsallis non- extensive
thermostatistics. We use this correspondence to generalize thermostatistics to
a large class of Kolmogorov-Nagumo means and suitably adapted definitions of
entropy.Comment: 4 pages revte
Mathematics of complexity in experimental high energy physics
Mathematical ideas and approaches common in complexity-related fields have
been fruitfully applied in experimental high energy physics also. We briefly
review some of the cross-pollination that is occurring.Comment: 7 pages, 3 figs, latex; Second International Conference on Frontier
Science: A Nonlinear World: The Real World, Pavia, Italy, 8-12 September 200
The distribution of height and diameter in random non-plane binary trees
This study is dedicated to precise distributional analyses of the height of
non-plane unlabelled binary trees ("Otter trees"), when trees of a given size
are taken with equal likelihood. The height of a rooted tree of size is
proved to admit a limiting theta distribution, both in a central and local
sense, as well as obey moderate as well as large deviations estimates. The
approximations obtained for height also yield the limiting distribution of the
diameter of unrooted trees. The proofs rely on a precise analysis, in the
complex plane and near singularities, of generating functions associated with
trees of bounded height
Detailed Classification of Swift's Gamma-Ray Bursts
Earlier classification analyses found three types of gamma-ray bursts (short,
long and intermediate in duration) in the BATSE sample. Recent works have shown
that these three groups are also present in the RHESSI and the BeppoSAX
databases. The duration distribution analysis of the bursts observed by the
Swift satellite also favors the three-component model. In this paper, we extend
the analysis of the Swift data with spectral information. We show, using the
spectral hardness and the duration simultaneously, that the maximum likelihood
method favors the three-component against the two-component model. The
likelihood also shows that a fourth component is not needed.Comment: Accepted for publication in The Astrophysical Journa
Positive maps, majorization, entropic inequalities, and detection of entanglement
In this paper, we discuss some general connections between the notions of
positive map, weak majorization and entropic inequalities in the context of
detection of entanglement among bipartite quantum systems. First, basing on the
fact that any positive map can
be written as the difference between two completely positive maps
, we propose a possible way to generalize the
Nielsen--Kempe majorization criterion. Then we present two methods of
derivation of some general classes of entropic inequalities useful for the
detection of entanglement. While the first one follows from the aforementioned
generalized majorization relation and the concept of the Schur--concave
decreasing functions, the second is based on some functional inequalities. What
is important is that, contrary to the Nielsen--Kempe majorization criterion and
entropic inequalities, our criteria allow for the detection of entangled states
with positive partial transposition when using indecomposable positive maps. We
also point out that if a state with at least one maximally mixed subsystem is
detected by some necessary criterion based on the positive map , then
there exist entropic inequalities derived from (by both procedures)
that also detect this state. In this sense, they are equivalent to the
necessary criterion [I\ot\Lambda](\varrho_{AB})\geq 0. Moreover, our
inequalities provide a way of constructing multi--copy entanglement witnesses
and therefore are promising from the experimental point of view. Finally, we
discuss some of the derived inequalities in the context of recently introduced
protocol of state merging and possibility of approximating the mean value of a
linear entanglement witness.Comment: the published version, 25 pages in NJP format, 6 figure
Generalised-Lorentzian Thermodynamics
We extend the recently developed non-gaussian thermodynamic formalism
\cite{tre98} of a (presumably strongly turbulent) non-Markovian medium to its
most general form that allows for the formulation of a consistent thermodynamic
theory. All thermodynamic functions, including the definition of the
temperature, are shown to be meaningful. The thermodynamic potential from which
all relevant physical information in equilibrium can be extracted, is defined
consistently. The most important findings are the following two: (1) The
temperature is defined exactly in the same way as in classical statistical
mechanics as the derivative of the energy with respect to the entropy at
constant volume. (2) Observables are defined in the same way as in Boltzmannian
statistics as the linear averages of the new equilibrium distribution function.
This lets us conclude that the new state is a real thermodynamic equilibrium in
systems capable of strong turbulence with the new distribution function
replacing the Boltzmann distribution in such systems. We discuss the ideal gas,
find the equation of state, and derive the specific heat and adiabatic exponent
for such a gas. We also derive the new Gibbsian distribution of states. Finally
we discuss the physical reasons for the development of such states and the
observable properties of the new distribution function.Comment: 13 pages, 1 figur
Statistical thermodynamics for choice models on graphs
Formalism based on equilibrium statistical thermodynamics is applied to
communication networks of decision making individuals. It is shown that in
statistical ensembles for choice models, properly defined disutility can play
the same role as energy in statistical mechanics. We demonstrate additivity and
extensivity of disutility and build three types of equilibrium statistical
ensembles: the canonical, the grand canonical and the super-canonical. Using
Boltzmann-like probability measure one reproduce the logit choice model. We
also propose using q-distributions for temperature evolution of moments of
stochastic variables. The formalism is applied to three network topologies of
different degrees of symmetry, for which in many cases analytic results are
obtained and numerical simulations are performed for all of them. Possible
applications of the model to airline networks and its usefulness for practical
support of economic decisions is pointed out.Comment: 17 pages, 13 figure
Cantor type functions in non-integer bases
Cantor's ternary function is generalized to arbitrary base-change functions
in non-integer bases. Some of them share the curious properties of Cantor's
function, while others behave quite differently
- …