Elementary linear algebra for advanced spectral problems

We discuss the general method of Grushin problems, closely related to Shur complements, Feshbach projections and effective Hamiltonians, and describe various appearances in spectral theory, pdes, mathematical physics and numerical problems.Comment: 2 figure

Measurement of heavy-flavor production in Pb-Pb collisions at the LHC with ALICE

A Large Ion Collider Experiment (ALICE) at the Large Hadron Collider (LHC) has been built in order to study the Quark-Gluon Plasma (QGP) created in high-energy nuclear collisions. As heavy-flavor quarks are produced at the early stage of the collision, they serve as sensitive probes for the QGP. The ALICE detector with its capabilities such as particle identification, secondary vertexing and tracking in a high multiplicity environment can address, among other measurements, the heavy-flavor sector in heavy-ion collisions. We present latest results on the measurement of the nuclear modification factor of open heavy-flavors as well as on the measurement of open heavy-flavor azimuthal anisotropy v2 in Pb-Pb collisions at sqrt(s) = 2.76 TeV. Open charmed hadrons are reconstructed in the hadronic decay channels D0->Kpi, D+->Kpipi, and D*+->D0pi applying a secondary decay-vertex topology. Complementary measurements are performed by detecting electrons (muons) from semi-leptonic decays of open heavy-flavor hadrons in the central (forward) rapidity region.Comment: 10 pages, 6 figures. Talk given by Robert Grajcarek at the 11th International Conference on Nucleus-Nucleus Collisions (NN2012), San Antonio, Texas, USA, May 27-June 1, 2012. To appear in the NN2012 Proceedings in Journal of Physics: Conference Series (JPCS

Strangeness enhancement from strong color fields at RHIC

In ultra-relativistic heavy ion collisions, early stage multiple scatterings may lead to an increase of the color electric field strength. Consequently, particle production - especially heavy quark (and di-quark) production - is greatly enhanced according to the Schwinger mechanism. We test this idea via the Ultra-relativistic Quantum Molecular Dynamics model (UrQMD) for Au+Au collisions at the full RHIC energy ($\sqrt{s} = 200$ AGeV). Relative to p+p collisions, a factor of 60, 20 and 7 enhancement respectively, for $\Omega$ ($sss$), $\Xi$ ($ss$), and $\Lambda$, $\Sigma$ ($s$) is predicted for a model with increased color electric field strength

Scaling violations: Connections between elastic and inelastic hadron scattering in a geometrical approach

Starting from a short range expansion of the inelastic overlap function, capable of describing quite well the elastic pp and $\bar{p}p$ scattering data, we obtain extensions to the inelastic channel, through unitarity and an impact parameter approach. Based on geometrical arguments we infer some characteristics of the elementary hadronic process and this allows an excellent description of the inclusive multiplicity distributions in $pp$ and $\bar{p}p$ collisions. With this approach we quantitatively correlate the violations of both geometrical and KNO scaling in an analytical way. The physical picture from both channels is that the geometrical evolution of the hadronic constituents is principally reponsible for the energy dependence of the physical quantities rather than the dynamical (elementary) interaction itself.Comment: 16 pages, aps-revtex, 11 figure