Elliptic flow of the dilute Fermi gas: From kinetics to hydrodynamics

We use the Boltzmann equation in the relaxation time approximation to study the expansion of a dilute Fermi gas at unitarity. We focus, in particular, on the approach to the hydrodynamic limit. Our main finding are: i) In the regime that has been studied experimentally hydrodynamic effects beyond the Navier-Stokes approximation are small, ii) mean field corrections to the Boltzmann equation are not important, iii) experimental data imply that freezeout occurs very late, that means that the relaxation time remains smaller than the expansion time during the entire evolution of the system, iv) the experimental results also imply that the bulk viscosity is significantly smaller than the shear viscosity of the system.Comment: 18 pages, 6 figure

Hydrodynamic fluctuations and the minimum shear viscosity of the dilute Fermi gas at unitarity

We study hydrodynamic fluctuations in a non-relativistic fluid. We show that in three dimensions fluctuations lead to a minimum in the shear viscosity to entropy density ratio $\eta/s$ as a function of the temperature. The minimum provides a bound on $\eta/s$ which is independent of the conjectured bound in string theory, $\eta/s \geq \hbar/(4\pi k_B)$, where $s$ is the entropy density. For the dilute Fermi gas at unitarity we find \eta/s\gsim 0.2\hbar. This bound is not universal -- it depends on thermodynamic properties of the unitary Fermi gas, and on empirical information about the range of validity of hydrodynamics. We also find that the viscous relaxation time of a hydrodynamic mode with frequency $\omega$ diverges as $1/\sqrt{\omega}$, and that the shear viscosity in two dimensions diverges as $\log(1/ \omega)$.Comment: 26 pages, 5 figures; final version to appear in Phys Rev

Calculation of the persistence length of a flexible polymer chain with short range self-repulsion

For a self-repelling polymer chain consisting of n segments we calculate the persistence length L(j,n), defined as the projection of the end-to-end vector on the direction of the j`th segment. This quantity shows some pronounced variation along the chain. Using the renormalization group and epsilon-expansion we establish the scaling form and calculate the scaling function to order epsilon^2. Asymptotically the simple result L(j,n) ~ const(j(n-j)/n)^(2nu-1) emerges for dimension d=3. Also outside the excluded volume limit L(j,n) is found to behave very similar to the swelling factor of a chain of length j(n-j)/n. We carry through simulations which are found to be in good accord with our analytical results. For d=2 both our and previous simulations as well as theoretical arguments suggest the existence of logarithmic anomalies.Comment: 28 pages, 8 figures, changed conten

Mass Terms in Effective Theories of High Density Quark Matter

We study the structure of mass terms in the effective theory for quasi-particles in QCD at high baryon density. To next-to-leading order in the $1/p_F$ expansion we find two types of mass terms, chirality conserving two-fermion operators and chirality violating four-fermion operators. In the effective chiral theory for Goldstone modes in the color-flavor-locked (CFL) phase the former terms correspond to effective chemical potentials, while the latter lead to Lorentz invariant mass terms. We compute the masses of Goldstone bosons in the CFL phase, confirming earlier results by Son and Stephanov as well as Bedaque and Sch\"afer. We show that to leading order in the coupling constant $g$ there is no anti-particle gap contribution to the mass of Goldstone modes, and that our results are independent of the choice of gauge.Comment: 22 pages, 4 figure

Production of Z^0 bosons with rapidity gaps: exclusive photoproduction in gamma p and p p collisions and inclusive double diffractive Z^0's

We extend the k_\perp-factorization formalism for exclusive photoproduction of vector mesons to the production of electroweak Z^0 bosons. Predictions for the gamma p \to Z^0 p and p p \to p p Z^0 reactions are given using an unintegrated gluon distribution tested against deep inelastic data. We present distributions in the Z^0 rapidity, transverse momentum of Z^0 as well as in relative azimuthal angle between outgoing protons. The contributions of different flavours are discussed. Absorption effects lower the cross section by a factor of 1.5-2, depending on the Z-boson rapidity. We also discuss the production of Z^0 bosons in central inclusive production. Here rapidity and (x_{\Pom,1}, x_{\Pom,2}) distributions of Z^0 are calculated. The corresponding cross section is about three orders of magnitude larger than that for the purely exclusive process.Comment: 19 pages, 14 figs, A. Cisek is married name of A. Rybarsk

Magnetic susceptibility of quark matter within Fermi-liquid theory

Possibility of spontaneous magnetization in QCD and magnetic properties of quark matter is discussed by evaluating the magnetic susceptibility within Fermi-liquid theory. The screening effects for gluons are taken into account to figure out the specific properties of the magnetic transition in gauge theories. It is shown that the static screening effect in terms of the Debye mass does not necessarily work against the magnetic instability; it promotes the instability, depending on the coupling constant and the number of flavors.Comment: 10 pages, 2 figure

Binary Black Hole Coalescence in Semi-Analytic Puncture Evolution

Binary black-hole coalescence is treated semi-analytically by a novel approach. Our prescription employs the conservative Skeleton Hamiltonian that describes orbiting Brill-Lindquist wormholes (termed punctures in Numerical Relativity) within a waveless truncation to the Einstein field equations [G. Faye, P. Jaranowski and G. Sch\"afer, Phys. Rev. D {\bf 69}, 124029 (2004)]. We incorporate, in a transparent Hamiltonian way and in Burke-Thorne gauge structure, the effects of gravitational radiation reaction into the above Skeleton dynamics with the help of 3.5PN accurate angular momentum flux for compact binaries in quasi-circular orbits to obtain a Semi-Analytic Puncture Evolution to model merging black-hole binaries. With the help of the TaylorT4 approximant at 3.5PN order, we perform a {\it first-order} comparison between gravitational wave phase evolutions in Numerical Relativity and our approach for equal-mass binary black holes. This comparison reveals that a modified Skeletonian reactive dynamics that employs flexible parameters will be required to prevent the dephasing between our scheme and Numerical Relativity, similar to what is pursued in the Effective One Body approach. A rough estimate for the gravitational waveform associated with the binary black-hole coalescence in our approach is also provided.Comment: 16 pages, 5 figure

Quantum criticality with a twist - interplay of correlations and Kohn anomalies in three dimensions

A general understanding of quantum phase transitions in strongly correlated materials is still lacking. By exploiting a cutting-edge quantum many-body approach, the dynamical vertex approximation, we make an important progress, determining the quantum critical properties of the antiferromagnetic transition in the fundamental model for correlated electrons, the Hubbard model in three dimensions. In particular, we demonstrate that -in contradiction to the conventional Hertz-Millis-Moriya theory- its quantum critical behavior is driven by the Kohn anomalies of the Fermi surface, even when electronic correlations become strong.Comment: 6 pages, 4 figures (8 pages Supplemental Material

Superdense Matter

We review recent work on the phase structure of QCD at very high baryon density. We introduce the phenomenon of color superconductivity and discuss the use of weak coupling methods. We study the phase structure as a function of the number of flavors and their masses. We also introduce effective theories that describe low energy excitations at high baryon density. Finally, we study the possibility of kaon condensation at very large baryon density.Comment: 13 pages, talk at ICPAQGP, Jaipur, India, Nov. 26-30, 2001; to appear in the proceeding