Particle states of Lattice QCD

We determine the degeneracy factor and the average particle mass of particles that produce the Lattice QCD pressure and specific entropy at zero baryon chemical potential. The number of states of the gluons and the quarks are found to converge above $T=$230 MeV to almost constant values, close to the number of states of an ideal Quark-Gluon Phase, while their assigned masses retain high values. The number of states and the average mass of a system containing quarks in interaction with gluons are found to decrease steeply with increase of temperature between $T \sim 150$ and 160 MeV, a region contained within the region of the chiral transition. The minimum value of the number of states within this temperature interval indicates that the states are of hadronic nature.Comment: 21 pages, 18 figure

On the push&pull protocol for rumour spreading

The asynchronous push&pull protocol, a randomized distributed algorithm for spreading a rumour in a graph $G$, works as follows. Independent Poisson clocks of rate 1 are associated with the vertices of $G$. Initially, one vertex of $G$ knows the rumour. Whenever the clock of a vertex $x$ rings, it calls a random neighbour $y$: if $x$ knows the rumour and $y$ does not, then $x$ tells $y$ the rumour (a push operation), and if $x$ does not know the rumour and $y$ knows it, $y$ tells $x$ the rumour (a pull operation). The average spread time of $G$ is the expected time it takes for all vertices to know the rumour, and the guaranteed spread time of $G$ is the smallest time $t$ such that with probability at least $1-1/n$, after time $t$ all vertices know the rumour. The synchronous variant of this protocol, in which each clock rings precisely at times $1,2,\dots$, has been studied extensively. We prove the following results for any $n$-vertex graph: In either version, the average spread time is at most linear even if only the pull operation is used, and the guaranteed spread time is within a logarithmic factor of the average spread time, so it is $O(n\log n)$. In the asynchronous version, both the average and guaranteed spread times are $\Omega(\log n)$. We give examples of graphs illustrating that these bounds are best possible up to constant factors. We also prove theoretical relationships between the guaranteed spread times in the two versions. Firstly, in all graphs the guaranteed spread time in the asynchronous version is within an $O(\log n)$ factor of that in the synchronous version, and this is tight. Next, we find examples of graphs whose asynchronous spread times are logarithmic, but the synchronous versions are polynomially large. Finally, we show for any graph that the ratio of the synchronous spread time to the asynchronous spread time is $O(n^{2/3})$.Comment: 25 page

The strange-quark chemical potential as an experimentally accessible "order parameter" of the deconfinement phase transition for finite baryon-density

We consider the change of the strange-quark chemical potential in the phase diagram of nuclear matter, employing the Wilson loop and scalar quark condensate order parameters, mass-scaled partition functions and enforcing flavor conservation. Assuming the region beyond the hadronic phase to be described by massive, correlated and interacting quarks, in the spirit of lattice and effective QCD calculations, we find the strange-quark chemical potential to change sign: from positive in the hadronic phase - to zero upon deconfinement - to negative in the partonic domain. We propose this change in the sign of the strange-quark chemical potential to be an experimentally accessible order parameter and a unique, concise and well-defined indication of the quark-deconfinement phase transition in nuclear matter.Comment: 22 pages, 14 figures within text, 2 figures(6,B3) as separate files. To be published in J.Phys.G: Nucl.&Part.Phys. G28 (2002

Model of Centauro and strangelet production in heavy ion collisions

We discuss the phenomenological model of Centauro event production in relativistic nucleus-nucleus collisions. This model makes quantitative predictions for kinematic observables, baryon number and mass of the Centauro fireball and its decay products. Centauros decay mainly to nucleons, strange hyperons and possibly strangelets. Simulations of Centauro events for the CASTOR detector in Pb-Pb collisions at LHC energies are performed. The signatures of these events are discussed in detail.Comment: 19 pages, LaTeX+revtex4, 14 eps-figures and 3 table

Physics at Very Small Angles with CASTOR at CMS

CASTOR is a small (56 cm diameter) quartz-tungsten Cerenkov calorimeter covering the small angles 0.2-0.6 deg (5.2<="eta"<=6.4) in CMS, a major experiment at the LHC. Particularly with heavy-ion reactions a substantial fraction of the total reaction energy goes into this large "eta" region. CASTOR will function as a part of CMS and also as an independent detector to search for special types of events in the far-forward region. It is divided into 16 azimuthal sectors, each with 18 longitudinal segments to allow identification of particles by their energy-loss profiles. The most forward segments are smaller to better characterize electromagnetic events

A study of the entanglement in systems with periodic boundary conditions

We define the local periodic linking number, LK, between two oriented closed or open chains in a system with three-dimensional periodic boundary conditions. The properties of LK indicate that it is an appropriate measure of entanglement between a collection of chains in a periodic system. Using this measure of linking to assess the extent of entanglement in a polymer melt we study the effect of CReTA algorithm on the entanglement of polyethylene chains. Our numerical results show that the statistics of the local periodic linking number observed for polymer melts before and after the application of CReTA are the same.Comment: 11 pages, 11 figure