Combinatorial Markov chains on linear extensions

We consider generalizations of Schuetzenberger's promotion operator on the set L of linear extensions of a finite poset of size n. This gives rise to a strongly connected graph on L. By assigning weights to the edges of the graph in two different ways, we study two Markov chains, both of which are irreducible. The stationary state of one gives rise to the uniform distribution, whereas the weights of the stationary state of the other has a nice product formula. This generalizes results by Hendricks on the Tsetlin library, which corresponds to the case when the poset is the anti-chain and hence L=S_n is the full symmetric group. We also provide explicit eigenvalues of the transition matrix in general when the poset is a rooted forest. This is shown by proving that the associated monoid is R-trivial and then using Steinberg's extension of Brown's theory for Markov chains on left regular bands to R-trivial monoids.Comment: 35 pages, more examples of promotion, rephrased the main theorems in terms of discrete time Markov chain

Transverse Fresnel-Fizeau drag effects in strongly dispersive media

A light beam normally incident upon an uniformly moving dielectric medium is in general subject to bendings due to a transverse Fresnel-Fizeau light drag effect. In conventional dielectrics, the magnitude of this bending effect is very small and hard to detect. Yet, it can be dramatically enhanced in strongly dispersive media where slow group velocities in the m/s range have been recently observed taking advantage of the electromagnetically induced transparency (EIT) effect. In addition to the usual downstream drag that takes place for positive group velocities, we predict a significant anomalous upstream drag to occur for small and negative group velocities. Furthermore, for sufficiently fast speeds of the medium, higher order dispersion terms are found to play an important role and to be responsible for peculiar effects such as light propagation along curved paths and the restoration of the spatial coherence of an incident noisy beam. The physics underlying this new class of slow-light effects is thoroughly discussed

Universal Behavior of Charged Particle Production in Heavy Ion Collisions

The PHOBOS experiment at RHIC has measured the multiplicity of primary charged particles as a function of centrality and pseudorapidity in Au+Au collisions at sqrt(s_NN) = 19.6, 130 and 200 GeV. Two kinds of universal behavior are observed in charged particle production in heavy ion collisions. The first is that forward particle production, over a range of energies, follows a universal limiting curve with a non-trivial centrality dependence. The second arises from comparisons with pp/pbar-p and e+e- data. N_tot/(N_part/2) in nuclear collisions at high energy scales with sqrt(s) in a similar way as N_tot in e+e- collisions and has a very weak centrality dependence. This feature may be related to a reduction in the leading particle effect due to the multiple collisions suffered per participant in heavy ion collisions.Comment: 4 Pages, 5 Figures, contributed to the Proceedings of Quark Matter 2002, Nantes, France, 18-24 July 200

Global Observations from PHOBOS

Particle production in Au+Au collisions has been measured in the PHOBOS experiment at RHIC for a range of collision energies. Three empirical observations have emerged from this dataset which require theoretical examination. First, there is clear evidence of limiting fragmentation. Namely, particle production in central Au+Au collisions, when expressed as $dN/d\eta'$ ($\eta' \equiv \eta-y_{beam}$), becomes energy independent at high energy for a broad region of $\eta'$ around $\eta'=0$. This energy-independent region grows with energy, allowing only a limited region (if any) of longitudinal boost-invariance. Second, there is a striking similarity between particle production in e+e- and Au+Au collisions (scaled by the number of participating nucleon pairs). Both the total number of produced particles and the longitudinal distribution of produced particles are approximately the same in e+e- and in scaled Au+Au. This observation was not predicted and has not been explained. Finally, particle production has been found to scale approximately with the number of participating nucleon pairs for $N_{part}>65$. This scaling occurs both for the total multiplicity and for high \pT particles (3 <\pT< 4.5 GeV/c).Comment: QM2002 plenary talk, 10 pages, 11 figure

Recent Results from PHOBOS at RHIC

The PHOBOS experiment at RHIC has recorded measurements for Au-Au collisions spanning nucleon-nucleon center-of-mass energies from 19.6 GeV to 200 GeV. Global observables such as elliptic flow and charged particle multiplicity provide important constraints on model predictions that characterize the state of matter produced in these collisions. The nearly 4 pi acceptance of the PHOBOS experiment provides excellent coverage for complete flow and multiplicity measurements. Results including beam energy and centrality dependencies are presented and compared to elementary systems.Comment: 4 pages, 4 figures, proceedings from PANIC02 in Osaka, Japa

Evidence of Final-State Suppression of High-p_T Hadrons in Au + Au Collisions Using d + Au Measurements at RHIC

Transverse momentum spectra of charged hadrons with ${p_{T} <}$ 6 GeV/c have been measured near mid-rapidity (0.2 $< \eta <$ 1.4) by the PHOBOS experiment at RHIC in Au + Au and d + Au collisions at ${\sqrt{s_{_{NN}}} = \rm {200 GeV}}$. The spectra for different collision centralities are compared to ${p + \bar{p}}$ collisions at the same energy. The resulting nuclear modification factor for central Au + Au collisions shows evidence of strong suppression of charged hadrons in the high-$p_{T}$ region (${>2}$ GeV/c). In contrast, the d + Au nuclear modification factor exhibits no suppression of the high-$p_{T}$ yields. These measurements suggest a large energy loss of the high-$p_{T}$ particles in the highly interacting medium created in the central Au + Au collisions. The lack of suppression in d + Au collisions suggests that it is unlikely that initial state effects can explain the suppression in the central Au + Au collisions.Comment: 3 pages, 4 figures, International Europhysics Conference on High Energy Physics EPS (July 17th-23rd 2003) in Aachen, German

Identified particles in Au+Au collisions at sqrt{s_NN} = 200 GeV

The yields of identified particles have been measured at RHIC for Au+Au collisions at sqrt{s_NN} = 200 GeV using the PHOBOS spectrometer. The ratios of antiparticle to particle yields near mid-rapidity are presented. The first measurements of the invariant yields of charged pions, kaons and protons at very low transverse momenta are also shown.Comment: 4 pages, 4 figures, Contribution to Quark Matter 2002, Nantes, France, July 200

Particle density fluctuations

Event-by-event fluctuations in the multiplicities of charged particles and photons at SPS energies are discussed. Fluctuations are studied by controlling the centrality of the reaction and rapidity acceptance of the detectors. Results are also presented on the event-by-event study of correlations between the multiplicity of charged particles and photons to search for DCC-like signals.Comment: Talk presented at Quark Matter 2002, Nantes, Franc

Search for DCC in 158A GeV Pb+Pb Collisions

A detailed analysis of the phase space distributions of charged particles and photons have been carried out using two independent methods. The results indicate the presence of nonstatistical fluctuations in localized regions of phase space.Comment: Talk at the PANIC99 Conference, June 9-16, 199

Present Status and Future of DCC Analysis

Disoriented Chiral Condensates (DCC) have been predicted to form in high energy heavy ion collisions where the approximate chiral symmetry of QCD has been restored. This leads to large imbalances in the production of charged to neutral pions. Sophisticated analysis methods are being developed to disentangle DCC events out of the large background of events with conventionally produced particles. We present a short review of current analysis methods and future prospects.Comment: 12 pages, 5 figures. Invited talk presented at the 13th International Conference on Ultrarelativistic Nucleus-Nucleus Collisions (Quark Matter 97), Tsukuba, Japan, 1-5 Dec 199