Multiparticle production processes from the Information Theory point of view

We look at multiparticle production processes from the Information Theory point of view, both in its extensive and nonextensive versions. Examples of both symmetric (like pp or AA) and asymmetric (like pA) collisions are considered showing that some ways of description of experimental data used in the literature are of more general validity than usually anticipated.}Comment: Talk given at 4th Budapest Winter School On Heavy Ion Physics (2004) 16 pages, 5 figures; version published in APH (HIP

Quantum Clan Model description of Bose Einstein Correlations

We propose a novel numerical method of modelling Bose-Einstein correlations (BEC) observed among identical (bosonic) particles produced in multiparticle production reactions. We argue that the most natural approach is to work directly in the momentum space in which the Bose statistics of secondaries reveals itself in their tendency to bunch in a specific way in the available phase space. Because such procedure is essentially identical to the clan model of multiparticle distributions proposed some time ago, therefore we call it the Quantum Clan Model.Comment: Talk given at 4th Budapest Winter School On Eavy Ion Physics (2004), 6 pages, two figures; version published in APH (HIP

On indecomposable normal matrices in spaces with indefinite scalar product

Finite dimensional linear spaces (both complex and real) with indefinite scalar product [.,.] are considered. Upper and lower bounds are given for the size of an indecomposable matrix that is normal with respect to this scalar product in terms of specific functions of v = min{v-, v+}, where v-, (v+) is the number of negative (positive) squares of the form [x,x]. All the bounds except for one are proved to be strict.Comment: 9 page

Nehari problems and equalizing vectors for infinite-dimensional systems

For a class of infinite-dimensional systems we obtain a simple frequency domain solution for the suboptimal Nehari extension problem. The approach is via $J$-spectral factorization, and it uses the concept of equalizing vectors. Moreover, the connection between the equalizing vectors and the Nehari extension problem is given. \u

J-spectral factorization and equalizing vectors

For the Wiener class of matrix-valued functions we provide necessary and sufficient conditions for the existence of a $J$-spectral factorization. One of these conditions is in terms of equalizing vectors. A second one states that the existence of a $J$-spectral factorization is equivalent to the invertibility of the Toeplitz operator associated to the matrix to be factorized. Our proofs are simple and only use standard results of general factorization theory. Note that we do not use a state space representation of the system. However, we make the connection with the known results for the Pritchard-Salamon class of systems where an equivalent condition with the solvability of an algebraic Riccati equation is given. For Riesz-spectral systems another necessary and sufficient conditions for the existence of a $J$-spectral factorization in terms of the Hamiltonian is added

On effective index approximations of photonic crystal slabs

As a means to assess the quality of effective index approximations in simulations of photonic crystal slabs, we consider a reduction of 2-D Helmholtz problems for waveguide Bragg gratings to 1-D wave propagation, and compare with rigorous 2-D reference solutions. Variational procedures permit to establish a reasonable effective index profile even in cases where locally no guided modes exist

Classification of normal operators in spaces with indefinite scalar product of rank 2

A finite-dimensional complex space with indefinite scalar product [.,.] having v- = 2 negative squares and v+ >= 2 positive ones is considered. The paper presents a classification of operators that are normal with respect to this product. It is related to the study by Gohberg and Reichstein in which a similar classification was obtained for the case v = min{v-, v+} = 1.Comment: 42 page