602 research outputs found
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
(), becomes energy independent at high energy for a
broad region of around . 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 . 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 6 GeV/c have
been measured near mid-rapidity (0.2 1.4) by the PHOBOS experiment
at RHIC in Au + Au and d + Au collisions at . The spectra for different collision centralities are compared to 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- region ( GeV/c). In contrast, the d +
Au nuclear modification factor exhibits no suppression of the high-
yields. These measurements suggest a large energy loss of the high-
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
- …