Einstein-Podolsky-Rosen correlations in a hybrid system

We calculate the relativistic correlation function for a hybrid system of a photon and a Dirac-particle. Such a system can be produced in decay of another spin-1/2 fermion. We show, that the relativistic correlation function, which depends on particle momenta, may have local extrema for fermion velocity of order 0.5 c. This influences the degree of violation of CHSH inequality.Comment: 9 pages, 6 figure

Single-Exponential FPT Algorithms for Enumerating Secluded F\mathcal{F}-Free Subgraphs and Deleting to Scattered Graph Classes

The celebrated notion of important separators bounds the number of small $(S,T)$-separators in a graph which are 'farthest from $S$' in a technical sense. In this paper, we introduce a generalization of this powerful algorithmic primitive that is phrased in terms of $k$-secluded vertex sets: sets with an open neighborhood of size at most $k$. In this terminology, the bound on important separators says that there are at most $4^k$ maximal $k$-secluded connected vertex sets $C$ containing $S$ but disjoint from $T$. We generalize this statement significantly: even when we demand that $G[C]$ avoids a finite set $\mathcal{F}$ of forbidden induced subgraphs, the number of such maximal subgraphs is $2^{O(k)}$ and they can be enumerated efficiently. This allows us to make significant improvements for two problems from the literature. Our first application concerns the 'Connected $k$-Secluded $\mathcal{F}$-free subgraph' problem, where $\mathcal{F}$ is a finite set of forbidden induced subgraphs. Given a graph in which each vertex has a positive integer weight, the problem asks to find a maximum-weight connected $k$-secluded vertex set $C \subseteq V(G)$ such that $G[C]$ does not contain an induced subgraph isomorphic to any $F \in \mathcal{F}$. The parameterization by $k$ is known to be solvable in triple-exponential time via the technique of recursive understanding, which we improve to single-exponential. Our second application concerns the deletion problem to scattered graph classes. Here, the task is to find a vertex set of size at most $k$ whose removal yields a graph whose each connected component belongs to one of the prescribed graph classes $\Pi_1, \ldots, \Pi_d$. We obtain a single-exponential algorithm whenever each class $\Pi_i$ is characterized by a finite number of forbidden induced subgraphs. This generalizes and improves upon earlier results in the literature.Comment: To appear at ISAAC'2

Some forgotten features of the Bose Einstein Correlations

Notwithstanding the visible maturity of the subject of Bose-Einstein Correlations (BEC), as witnessed nowadays, we would like to bring to ones attention two points, which apparently did not received attention they deserve: the problem of the choice of the form of $C_2(Q)$ correlation function when effects of partial coherence of the hadronizing source are to be included and the feasibility to model effects of Bose-Einstein statistics, in particular the BEC, by direct numerical simulations.Comment: Talk delivered by G.Wilk at the International Workshop {\it Relativistic Nuclear Physics: from Nuclotron to LHC energies}, Kiev, June 18-22, 2007, Ukraine; misprints correcte

Techniques for the study of singularities with applications to resolution of 2-dimensional schemes

We give an overview of invariants of algebraic singularities over perfect fields. We then show how they lead to a synthetic proof of embedded resolution of singularities of 2-dimensional schemes.Comment: 26 pages; minor changes have been adde

Thin silica films on Ru(0001): monolayer, bilayer and three-dimensional networks of [SiO₄] tetrahedra

The atomic structure of thin silica films grown over a Ru(0001) substrate was studied by X-ray photoelectron spectroscopy, infrared reflection absorption spectroscopy, low energy electron diffraction, helium ion scattering spectroscopy, CO temperature programmed desorption, and scanning tunneling microscopy in combination with density functional theory calculations. The films were prepared by Si vapor deposition and subsequent oxidation at high temperatures. The silica film first grows as a monolayer of corner-sharing [SiO4] tetrahedra strongly bonded to the Ru(0001) surface through the Si–O–Ru linkages. At increasing amounts of Si, the film forms a bilayer of corner-sharing [SiO4] tetrahedra which is weakly bonded to Ru(0001). The bilayer film can be grown in either the crystalline or vitreous state, or both coexisting. Further increasing the film thickness leads to the formation of vitreous silica exhibiting a three-dimensional network of [SiO4]. The principal structure of the films can be monitored by infrared spectroscopy, as each structure shows a characteristic vibrational band, i.e., [similar]1135 cm-1 for a monolayer film, [similar]1300 cm⁻-1 for the bilayer structures, and [similar]1250 cm⁻-1 for the bulk-like vitreous silica

On the possible space-time fractality of the emitting source

Using simple space-time implementation of the random cascade model we investigate numerically a conjecture made some time ago which was joining the intermittent behaviour of spectra of emitted particles with the possible fractal structure of the emitting source. We demonstrate that such details are seen, as expected, in the Bose-Einstein correlations between identical particles. \\Comment: Thoroughly rewritten and modify version, to be published in Phys. Rev.

Production of deuterium, tritium, and 3^3He in central Pb+Pb collisions at 20A, 30A, 40A, 80A, and 158A GeV at the CERN SPS

Production of $d$, $t$, and $^3$He nuclei in central Pb+Pb interactions was studied at five collision energies ($\sqrt{s_{NN}}=$ 6.3, 7.6, 8.8, 12.3, and 17.3 GeV) with the NA49 detector at the CERN SPS. Transverse momentum spectra, rapidity distributions, and particle ratios were measured. Yields are compared to predictions of statistical models. Phase-space distributions of light nuclei are discussed and compared to those of protons in the context of a coalescence approach. The coalescence parameters $B_2$ and $B_3$, as well as coalescence radii for $d$ and $^3$He were determined as a function of transverse mass at all energies.Comment: 22 pages, 29 figures, 8 tables, for submission to Phys. Rev.