Probing the QCD phase diagram with fluctuations

The relevance of higher order cumulants of conserved charges for the analysis of freeze-out and critical conditions in heavy ion collisions at LHC and RHIC is discussed. Using properties of $O(4)$ scaling functions, the generic structure of these higher cumulants at vanishing baryon chemical potential is discussed. Chiral model calculations are then used to study their properties at non-zero baryon chemical potential. It is argued that the rapid variation of sixth and higher order cumulants at the phase boundary may be used to explore the QCD phase diagram in experiment. Moreover, results for the Polyakov loop susceptibilities in SU(3) lattice gauge theory as well as in (2+1) flavor lattice QCD are discussed. An analysis of the ratios of susceptibilities indicates that the deconfinement transition is reflected in characteristic modifications of these ratios.Comment: 14 pages, 6 figures. To appear in the G.E. Brown memorial volume in NP

Meson-nucleon scattering and vector mesons in nuclear matter

The properties of vector mesons in nuclear matter are discussed. I examine the constraints imposed by elementary processes on the widths of $\rho$ and $\omega$ mesons in nuclear matter. Furthermore, results for the $\rho$- and $\omega$-nucleon scattering amplitudes obtained by fitting meson-nucleon scattering data in a coupled-channel approach are presented.Comment: 7 pages, 6 EPS figures, uses appb.sty (included), talk given at Meson98, Cracow, May 98, to be published in Acta Physica Polonica

Three-body interactions in Fermi systems

We show that the contributions of three-quasiparticle interactions to normal Fermi systems at low energies and temperatures are suppressed by n_q/n compared to two-body interactions, where n_q is the density of excited or added quasiparticles and n is the ground-state density. For finite Fermi systems, three-quasiparticle contributions are suppressed by the corresponding ratio of particle numbers N_q/N. This is illustrated for polarons in strongly interacting spin-polarized Fermi gases and for valence neutrons in neutron-rich calcium isotopes.Comment: 16 pages, 1 figure; to appear in Festschrift on the occasion of Gerry Brown's 85th birthday, Ed. Sabine Lee (World Scientific

P-Wave Polarization of the ρ\rho-Meson and the Dilepton Spectrum in Dense Matter

We study the $p$-wave polarization operator of the $\rho$-meson due to $\rho N$ interactions via the $N^*$ (1720) and $\Delta (1905)$ resonances and compute the corresponding production rate for $e^+e^-$-pairs at finite temperature and baryon density. At high baryon density we find a significant shift of the spectrum to lower invariant masses.Comment: 22 pages, 8 Postscript figures, uses article.sty, epsf.sty, epsfig.st

Hamiltonian Flow Equations for the Lipkin Model

We derive Hamiltonian flow equations giving the evolution of the Lipkin Hamiltonian to a diagonal form using continuous unitary transformations. To close the system of flow equations, we present two different schemes. First we linearize an operator with three pairs of creation and destruction operators by reducing it to the $z$ component of the quasi spin. We obtain the well known RPA-result in the limit of large particle number. In the second scheme we introduce a new operator which improves the resulting spectrum considerably especially for few particles.Comment: 10 pages, 2 eps figures, uses article.sty, epsfig.st

Weak and strong coupling limits of the Boltzmann equation in the relaxation-time approximation

We consider a momentum dependent relaxation time for the Boltzmann equation in the relaxation time approximation. We employ a power law parametrization for the momentum dependence of the relaxation time, and calculate the shear and bulk viscosity, as well as, the charge and heat conductivity. We show, that for the two popular parametrizations, referred to as the linear and quadratic ansatz, one can obtain transport coefficients which corresponds to the weak and strong coupling regimes, respectively. We also show that, for a system of massless particles with vanishing chemical potential, the off-equilibrium corrections to the phase-space distribution function calculated with the quadratic ansatz are identical with those of the Grad's 14-moment method.Comment: 6 page

Susceptibilities and the Phase Structure of a Chiral Model with Polyakov Loops

In an extension of the Nambu-Jona-Lasinio model where the quarks interact with the temporal gluon field, represented by the Polyakov loop, we explore the relation between the deconfinement and chiral phase transitions. The effect of Polyakov loop dynamics on thermodynamic quantities, on the phase structure at finite temperature and baryon density and on various susceptibilities is presented. Particular emphasis is put on the behavior and properties of the fluctuations of the (approximate) order parameters and their dependence on temperature and net--quark number density. We also discuss how the phase structure of the model is influenced by the coupling of the quarks to the Polyakov loop.Comment: 18 pages, 22 figures; text rearranged and references added. results and conclusions unchanged; final version accepted for publication in Phys. Rev.