Lubricated friction between incommensurate substrates

This paper is part of a study of the frictional dynamics of a confined solid lubricant film - modelled as a one-dimensional chain of interacting particles confined between two ideally incommensurate substrates, one of which is driven relative to the other through an attached spring moving at constant velocity. This model system is characterized by three inherent length scales; depending on the precise choice of incommensurability among them it displays a strikingly different tribological behavior. Contrary to two length-scale systems such as the standard Frenkel-Kontorova (FK) model, for large chain stiffness one finds that here the most favorable (lowest friction) sliding regime is achieved by chain-substrate incommensurabilities belonging to the class of non-quadratic irrational numbers (e.g., the spiral mean). The well-known golden mean (quadratic) incommensurability which slides best in the standard FK model shows instead higher kinetic-friction values. The underlying reason lies in the pinning properties of the lattice of solitons formed by the chain with the substrate having the closest periodicity, with the other slider.Comment: 14 pagine latex - elsart, including 4 figures, submitted to Tribology Internationa

Spectroscopy of resonance decays in high-energy heavy-ion collisions

Invariant mass distributions of the hadronic decay products from resonances formed in relativistic heavy ion collision (RHIC) experiments are investigated with a view to disentangle the effects of thermal motion and the phase space of decay products from those of intrinsic changes in the structure of resonances at the freeze-out conditions. Analytic results of peak mass shifts for the cases of both equal and unequal mass decay products are derived. The shift is expressed in terms of the peak mass and width of the vacuum or medium-modified spectral functions and temperature. Examples of expected shifts in meson (e.g., rho, omega, and sigma) and baryon (e.g., Delta) resonances that are helpful to interpret recent RHIC measurements at BNL are provided. Although significant downward mass shifts are caused by widened widths of the $\rho-$meson in medium, a downward shift of at least 50 MeV in its intrinsic mass is required to account for the reported downward shift of 60-70 MeV in the peak of the rho-invariant mass distribution. An observed downward shift from the vacuum peak value of the Delta distinctively signals a significant downward shift in its intrinsic peak mass, since unlike for the rho-meson, phase space functions produce an upward shift for the Delta isobar.Comment: published version with slight change of title and some typos corrected, 12 pages, 5 figure

Evolution of Fluctuation in relativistic heavy-ion collisions

We have studied the time evolution of the fluctuations in the net baryon number for different initial conditions and space time evolution scenarios. We observe that the fluctuations at the freeze-out depend crucially on the equation of state (EOS) of the system and for realistic EOS the initial fluctuation is substantially dissipated at the freeze-out stage. At SPS energies the fluctuations in net baryon number at the freeze-out stage for quark gluon plasma and hadronic initial state is close to the Poissonian noise for ideal as well as for EOS obtained by including heavier hadronic degrees of freedom. For EOS obtained from the parametrization of lattice QCD results the fluctuation is larger than Poissonian noise. It is also observed that at RHIC energies the fluctuations at the freeze-out point deviates from the Poissonian noise for ideal as well as realistic equation of state, indicating presence of dynamical fluctuations.Comment: 9 pages and 6 figures (Major modifications done

Lattice Point Generating Functions and Symmetric Cones

We show that a recent identity of Beck-Gessel-Lee-Savage on the generating function of symmetrically contrained compositions of integers generalizes naturally to a family of convex polyhedral cones that are invariant under the action of a finite reflection group. We obtain general expressions for the multivariate generating functions of such cones, and work out the specific cases of a symmetry group of type A (previously known) and types B and D (new). We obtain several applications of the special cases in type B, including identities involving permutation statistics and lecture hall partitions.Comment: 19 page

A Mean Field Theory of the Chiral Phase Transition

The recent discussions by Koci\'c and Kogut on the nature of the chiral phase transition are reviewed. The mean-field nature of the transition suggested by these authors is supported in random matrix theory by Verbaarschot and Jackson which reproduces many aspects of QCD lattice simulations. In this paper, we point out physical arguments that favor a mean-field transition, not only for zero density and high temperature, but also for finite density. We show, using the Gross-Neveu model in 3 spatial dimensions in mean-field approximation, how the phase transition is constructed. In order to reproduce the lowering of the $\rho=0$, $T=0$ vacuum evaluated in lattice calculations, we introduce {nucleons} rather than constituent quarks in negative energy states, down to a momentum cut-off of $\Lambda$. We also discuss Brown-Rho scaling of the hadron masses in relation to the QCD phase transition, and how this scaling affects the CERES and HELIOS-3 dilepton experiments.Comment: 23 pages, Latex, no figure

Dilepton Production at SPS-energy Heavy Ion Collisions

The production of dileptons is studied within a hadronic transport model. We investigate the sensitivity of the dilepton spectra to the initial configuration of the hadronic phase in a ultrarelativistic heavy ion collision. Possible in medium correction due to the modifications of pions and the pion form factor in a hadronic gas are discussed.Comment: Dedicated to Gerry Brown in honor of the 32nd celebration of his 39th birthday. 31 pages Latex including 13 eps-figures, uses psfig.sty and epsf.st

Chiral Symmetry Restoration and the Georgi Vector Limit

The chiral phase transition at high temperature and/or density is interpreted in terms of Georgi's vector limit. We discuss three cases as possible support for this scenario: Quark-number susceptibility, cool kaons in heavy-ion process and an instanton-molecule picture for chiral restoration. Both the notion of ``mended symmetry" and the Georgi vector limit are suggested to be relevant in nuclear physics of dense matter.Comment: LATEX, 12 pages (no figures), SUNY NTG-94-44 (typos corrected

Do the Unidentified EGRET Sources Trace Annihilating Dark Matter in the Local Group?

In a cold dark matter (CDM) framework of structure formation, the dark matter haloes around galaxies assemble through successive mergers with smaller haloes. This merging process is not completely efficient, and hundreds of surviving halo cores, or {\it subhaloes}, are expected to remain in orbit within the halo of a galaxy like the Milky Way. While the dozen visible satellites of the Milky Way may trace some of these subhaloes, the majority are currently undetected. A large number of high-velocity clouds (HVCs) of neutral hydrogen {\it are} observed around the Milky Way, and it is plausible that some of the HVCs may trace subhaloes undetected in the optical. Confirming the existence of concentrations of dark matter associated with even a few of the HVCs would represent a dramatic step forward in our attempts to understand the nature of dark matter. Supersymmetric (SUSY) extensions of the Standard Model of particle physics currently suggest neutralinos as a natural well-motivated candidate for the non-baryonic dark matter of the universe. If this is indeed the case, then it may be possible to detect dark matter indirectly as it annihilates into neutrinos, photons or positrons. In particular, the centres of subhaloes might show up as point sources in gamma-ray observations. In this work we consider the possibility that some of the unidentified EGRET $\gamma$-ray sources trace annihilating neutralino dark matter in the dark substructure of the Local Group. We compare the observed positions and fluxes of both the unidentified EGRET sources and the HVCs with the positions and fluxes predicted by a model of halo substructure, to determine to what extent any of these three populations could be associated.Comment: 12 Pages, 4 figures, to appear in a special issue of ApSS. Presented at "The Multiwavelength Approach to Unidentified Gamma-Ray Sources" (Hong Kong, June 1 - 4, 2004; Conference organizers: K.S. Cheng and G.E. Romero

Baxter Q-operator and Separation of Variables for the open SL(2,R) spin chain

We construct the Baxter Q-operator and the representation of the Separated Variables (SoV) for the homogeneous open SL(2,R) spin chain. Applying the diagrammatical approach, we calculate Sklyanin's integration measure in the separated variables and obtain the solution to the spectral problem for the model in terms of the eigenvalues of the Q-operator. We show that the transition kernel to the SoV representation is factorized into the product of certain operators each depending on a single separated variable. As a consequence, it has a universal pyramid-like form that has been already observed for various quantum integrable models such as periodic Toda chain, closed SL(2,R) and SL(2,C) spin chains.Comment: 29 pages, 9 figures, Latex styl

Effects of in-medium vector meson masses on low-mass dileptons from SPS heavy-ion collisions

Using a relativistic transport model to describe the expansion of the fire-cylinder formed in the initial stage of heavy-ion collisions at SPS/CERN energies, we study the production of dileptons with mass below about 1 GeV from these collisions. The initial hadron abundance and their momentum distributions in the fire-cylinder are determined by following the general features of the results from microscopic models based on the string dynamics and further requiring that the final proton and pion spectra and rapidity distributions are in agreement with available experimental data. For dilepton production, we include the Dalitz decay of $\pi ^0$, $\eta$, $\eta^\prime$, $\omega$ and $a_1$ mesons, the direct decay of primary $\rho ^0$, $\omega$ and $\phi$ mesons, and the pion-pion annihilation that proceeds through the $\rho^0$ meson, the pion-rho annihilation that proceeds through the $a_1$ meson, and the kaon-antikaon annihilation that proceeds through the $\phi$ meson. We find that the modification of vector meson properties, especially the decrease of their mass due to the partial restoration of chiral symmetry, in hot and dense hadronic matter, provides a quantitative explanation of the recently observed enhancement of low-mass dileptons by the CERES collaboration in central S+Au collisions and by the HELIOS-3 collaboration in central S+W collisions.Comment: 46 pages, LaTeX, figures available from [email protected], to appear in Nucl. Phys.