Hadronic Equation of State and Speed of Sound in Thermal and Dense Medium

The equation of state $p(\epsilon)$ and speed of sound squared $c_s^2$ are studied in grand canonical ensemble of all hadron resonances having masses $\leq 2\,$GeV. This large ensemble is divided into strange and non-strange hadron resonances and furthermore to pionic, bosonic and femionic sectors. It is found that the pions represent the main contributors to $c_s^2$ and other thermodynamic quantities including the equation of state $p(\epsilon)$ at low temperatures. At high temperatures, the main contributions are added in by the massive hadron resonances. The speed of sound squared can be calculated from the derivative of pressure with respect to the energy density, $\partial p/\partial \epsilon$, or from the entropy-specific heat ratio, $s/c_v$. It is concluded that the physics of these two expressions is not necessarily identical. They are distinguishable below and above the critical temperature $T_c$. This behavior is observed at vanishing and finite chemical potential. At high temperatures, both expressions get very close to each other and both of them approach the asymptotic value, $1/3$. In the HRG results, which are only valid below $T_c$, the difference decreases with increasing the temperature and almost vanishes near $T_c$. It is concluded that the HRG model can very well reproduce the results of the lattice quantum chromodynamics (QCD) of $\partial p/\partial \epsilon$ and $s/c_v$, especially at finite chemical potential. In light of this, energy fluctuations and other collective phenomena associated with the specific heat might be present in the HRG model. At fixed temperatures, it is found that $c_s^2$ is not sensitive to the chemical potential.Comment: 19 pages, 6 figures with 13 eps graph

The Hagedorn temperature Revisited

The Hagedorn temperature, T_H is determined from the number of hadronic resonances including all mesons and baryons. This leads to a stable result T_H = 174 MeV consistent with the critical and the chemical freeze-out temperatures at zero chemical potential. We use this result to calculate the speed of sound and other thermodynamic quantities in the resonance hadron gas model for a wide range of baryon chemical potentials following the chemical freeze-out curve. We compare some of our results to those obtained previously in other papers.Comment: 13 pages, 4 figure

Indirect Evidence for L\'evy Walks in Squeeze Film Damping

Molecular flow gas damping of mechanical motion in confined geometries, and its associated noise, is important in a variety of fields, including precision measurement, gravitational wave detection, and MEMS devices. We used two torsion balance instruments to measure the strength and distance-dependence of `squeeze film' damping. Measured quality factors derived from free decay of oscillation are consistent with gas particle superdiffusion in L\'evy walks and inconsistent with those expected from traditional Gaussian random walk particle motion. The distance-dependence of squeeze film damping observed in our experiments is in agreement with a parameter-free Monte Carlo simulation. The squeeze film damping of the motion of a plate suspended a distance d away from a parallel surface scales with a fractional power between 1/d and 1/d^2.Comment: 5 pages 5 figures accepted for PRD; typo in equation 3 and figure 1 fixe

Strangeness, Equilibration, Hadronization

In these remarks I explain the motivation which leads us to consider chemical nonequilibrium processes in flavor equilibration and in statistical hadroniziation of quark--gluon plasma (QGP). Statistical hadronization allowing for chemical non-equilibrium is introduced. The reesults of fits to RHIC-130 results, including multistrange hadrons, are shown to agree only with the model of an exploding QGP fireball.Comment: 8 pages including one figure, discussion contribution at Strange Quark Matter 2001, Frankfurt, submitted to J. Phys.

Quantum Collective QCD String Dynamics

The string breaking model of particle production is extended in order to help explain the transverse momentum distribution in elementary collisions. Inspired by an idea of Bialas', we treat the string using a collective coordinate approach. This leads to a chromo-electric field strength which fluctuates, and in turn implies that quarks are produced according to a thermal distribution.Comment: 6 pages. Presented at SQM 2006. Submitted to J. Phys. G for publication in proceedings. Vers. 2: Minor revisions; final hadron spectrum calculation include

Spectrum and thermodynamic properties of two-dimensional N=(1,1) super Yang-Mills theory with fundamental matter and a Chern-Simons term

We consider N=(1,1) super Yang-Mills theory in 1+1 dimensions with fundamentals at large-N_c. A Chern-Simons term is included to give mass to the adjoint partons. Using the spectrum of the theory, we calculate thermodynamic properties of the system as a function of the temperature and the Yang-Mills coupling. In the large-N_c limit there are two non-communicating sectors, the glueball sector, which we presented previously, and the meson-like sector that we present here. We find that the meson-like sector dominates the thermodynamics. Like the glueball sector, the meson sector has a Hagedorn temperature T_H, and we show that the Hagedorn temperature grows with the coupling. We calculate the temperature and coupling dependence of the free energy for temperatures below T_H. As expected, the free energy for weak coupling and low temperature grows quadratically with the temperature. Also the ratio of the free energies at strong coupling compared to weak coupling, r_{s-w}, for low temperatures grows quadratically with T. In addition, our data suggest that r_{s-w} tends to zero in the continuum limit at low temperatures.Comment: 34 p

Avoided crossings in mesoscopic systems: electron propagation on a non-uniform magnetic cylinder

We consider an electron constrained to move on a surface with revolution symmetry in the presence of a constant magnetic field $B$ parallel to the surface axis. Depending on $B$ and the surface geometry the transverse part of the spectrum typically exhibits many crossings which change to avoided crossings if a weak symmetry breaking interaction is introduced. We study the effect of such perturbations on the quantum propagation. This problem admits a natural reformulation to which tools from molecular dynamics can be applied. In turn, this leads to the study of a perturbation theory for the time dependent Born-Oppenheimer approximation

Particle Ratios as a Probe of the QCD Critical Temperature

We show how the measured particle ratios can be used to provide non-trivial information about the critical temperature of the QCD phase transition. This is obtained by including the effects of highly massive Hagedorn resonances on statistical models, which are used to describe hadronic yields. The inclusion of Hagedorn states creates a dependence of the thermal fits on the Hagedorn temperature, $T_H$, which is assumed to be equal to $T_c$, and leads to an overall improvement of thermal fits. We find that for Au+Au collisions at RHIC at $\sqrt{s_{NN}}=200$ GeV the best square fit measure, $\chi^2$, occurs at $T_c \sim 176$ MeV and produces a chemical freeze-out temperature of 172.6 MeV and a baryon chemical potential of 39.7 MeV.Comment: 6 pages, 4 figure

High Temperature Limit of the N=2 N= 2 IIA Matrix Model

The high temperature limit of a system of two D-0 branes is investigated. The partition function can be expressed as a power series in $\beta$ (inverse temperature). The leading term in the high temperature expression of the partition function and effective potential is calculated {\em exactly}. Physical quantities like the mean square separation can also be exactly determined in the high temperature limit. We comment on SU(3) IIB matrix model and the difficulties to study it.Comment: Lattice 2000 (Gravity and Matrix Models

N=(1,1) super Yang--Mills theory in 1+1 dimensions at finite temperature

We present a formulation of N=(1,1) super Yang-Mills theory in 1+1 dimensions at finite temperature. The partition function is constructed by finding a numerical approximation to the entire spectrum. We solve numerically for the spectrum using Supersymmetric Discrete Light-Cone Quantization (SDLCQ) in the large-N_c approximation and calculate the density of states. We find that the density of states grows exponentially and the theory has a Hagedorn temperature, which we extract. We find that the Hagedorn temperature at infinite resolution is slightly less than one in units of (g^(2) N_c/pi)^(1/2). We use the density of states to also calculate a standard set of thermodynamic functions below the Hagedorn temperature. In this temperature range, we find that the thermodynamics is dominated by the massless states of the theory.Comment: 16 pages, 8 eps figures, LaTe