481 research outputs found
Maximum entropy and the problem of moments: A stable algorithm
We present a technique for entropy optimization to calculate a distribution
from its moments. The technique is based upon maximizing a discretized form of
the Shannon entropy functional by mapping the problem onto a dual space where
an optimal solution can be constructed iteratively. We demonstrate the
performance and stability of our algorithm with several tests on numerically
difficult functions. We then consider an electronic structure application, the
electronic density of states of amorphous silica and study the convergence of
Fermi level with increasing number of moments.Comment: 4 pages including 3 figure
Coherent states of a charged particle in a uniform magnetic field
The coherent states are constructed for a charged particle in a uniform
magnetic field based on coherent states for the circular motion which have
recently been introduced by the authors.Comment: 2 eps figure
Cellular Automata and Ultra-Discrete Painlev\'e Equations
Starting from integrable cellular automata we present a novel form of
Painlev\'e equations. These equations are discrete in both the independent
variable and the dependent one. We show that they capture the essence of the
behavior of the Painlev\'e equations organizing themselves into a coalescence
cascade and possessing special solutions. A necessary condition for the
integrability of cellular automata is also presented.Comment: 8 pages, plainTeX, 2 figure
Vector Continued Fractions using a Generalised Inverse
A real vector space combined with an inverse for vectors is sufficient to
define a vector continued fraction whose parameters consist of vector shifts
and changes of scale. The choice of sign for different components of the vector
inverse permits construction of vector analogues of the Jacobi continued
fraction. These vector Jacobi fractions are related to vector and scalar-valued
polynomial functions of the vectors, which satisfy recurrence relations similar
to those of orthogonal polynomials. The vector Jacobi fraction has strong
convergence properties which are demonstrated analytically, and illustrated
numerically.Comment: Published form - minor change
Real-variables characterization of generalized Stieltjes functions
We obtain a characterization of generalized Stieltjes functions of any order
\lambda > 0 in terms of inequalities for their derivatives on (0,\infty). When
\lambda=1, this provides a new and simple proof of a characterization of
Stieltjes functions first obtained by Widder in 1938.Comment: LaTeX2e, 9 pages. Version 2 contains some improvements in the
exposition suggested by a referee. To be published in Expositiones
Mathematica
Generating GHZ state in 2m-qubit spin network
We consider a pure 2m-qubit initial state to evolve under a particular
quantum me- chanical spin Hamiltonian, which can be written in terms of the
adjacency matrix of the Johnson network J(2m;m). Then, by using some techniques
such as spectral dis- tribution and stratification associated with the graphs,
employed in [1, 2], a maximally entangled GHZ state is generated between the
antipodes of the network. In fact, an explicit formula is given for the
suitable coupling strengths of the hamiltonian, so that a maximally entangled
state can be generated between antipodes of the network. By using some known
multipartite entanglement measures, the amount of the entanglement of the final
evolved state is calculated, and finally two examples of four qubit and six
qubit states are considered in details.Comment: 22 page
Quantum central limit theorem for continuous-time quantum walks on odd graphs in quantum probability theory
The method of the quantum probability theory only requires simple structural
data of graph and allows us to avoid a heavy combinational argument often
necessary to obtain full description of spectrum of the adjacency matrix. In
the present paper, by using the idea of calculation of the probability
amplitudes for continuous-time quantum walk in terms of the quantum probability
theory, we investigate quantum central limit theorem for continuous-time
quantum walks on odd graphs.Comment: 19 page, 1 figure
Pertussis infection in fully vaccinated children in day-care centers, Israel.
We tested 46 fully vaccinated children in two day-care centers in Israel who were exposed to a fatal case of pertussis infection. Only two of five children who tested positive for Bordetella pertussis met the World Health Organization's case definition for pertussis. Vaccinated children may be asymptomatic reservoirs for infection
Densities of States, Moments, and Maximally Broken Time-Reversal Symmetry
Power moments, modified moments, and optimized moments are powerful tools for
solving microscopic models of macroscopic systems; however the expansion of the
density of states as a continued fraction does not converge to the macroscopic
limit point-wise in energy with increasing numbers of moments. In this work the
moment problem is further constrained by minimal lifetimes or maximal breaking
of time-reversal symmetry, to yield approximate densities of states with
point-wise macroscopic limits. This is applied numerically to models with one
and two finite bands with various singularities, as well as to a model with
infinite band-width, and the results are compared with the maximum entropy
approximation where possible.Comment: Accepted for publication in Physical Review
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