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

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

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

Phases of QCD at High Baryon Density

We review recent work on the phase structure of QCD at very high baryon density. We introduce the phenomenon of color superconductivity and discuss how the quark masses and chemical potentials determine the structure of the superfluid quark phase. We comment on the possibility of kaon condensation at very high baryon density and study the competition between superfluid, density wave, and chiral crystal phases at intermediate density.Comment: 15 pages. To appear in the proceedings of the ECT Workshop on Neutron Star Interiors, Trento, Italy, June 200

Allometry and growth of eight tree taxa in United Kingdom woodlands.

This work is licensed under a Creative Commons Attribution 4.0 International License. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in the credit line; if the material is not included under the Creative Commons license, users will need to obtain permission from the license holder to reproduce the material. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0As part of a project to develop predictive ecosystem models of United Kingdom woodlands we have collated data from two United Kingdom woodlands - Wytham Woods and Alice Holt. Here we present data from 582 individual trees of eight taxa in the form of summary variables relating to the allometric relationships between trunk diameter, height, crown height, crown radius and trunk radial growth rate to the tree's light environment and diameter at breast height. In addition the raw data files containing the variables from which the summary data were obtained. Large sample sizes with longitudinal data spanning 22 years make these datasets useful for future studies concerned with the way trees change in size and shape over their life-span

On Color Superconductivity in External Magnetic Field

We study color superconductivity in external magnetic field. We discuss the reason why the mixing angles in color-flavor locked (CFL) and two-flavor superconductivity (2SC) phases are different despite the fact that the CFL gap goes to the 2SC gap for $m_s \to \infty$. Although flavor symmetry is explicitly broken in external magnetic field, we show that all values of gaps in their coset spaces of possible solutions in the CFL phase are equivalent in external magnetic field.Comment: 12 pages, LaTe

Instantons and Scalar Multiquark States: From Small to Large N_c

We study scalar quark-anti-quark and two-quark-two-anti-quark correlation functions in the instanton liquid model. We show that the instanton liquid supports a light scalar-isoscalar (sigma) meson, and that this state is strongly coupled to both $(\bar{q}q)$ and $(\bar{q}q)^2$. The scalar-isovector $a_0$ meson, on the other hand, is heavy. We also show that these properties are specific to QCD with three colors. In the large $N_c$ limit the scalar-isoscalar meson is not light, and it is mainly coupled to $(\bar{q}q)$.Comment: 24 page

On the Scattering Phase for AdS_5 x S^5 Strings

We propose a phase factor of the worldsheet S-matrix for strings on AdS_5 x S^5 apparently solving Janik's crossing relation.Comment: 9 pages, v2: revised conclusions about agreement with perturbative string theory; minor changes, v3: resolution to above problems indicated, to appear in Mod. Phys. Lett.