Fermi systems with long scattering lengths

Ground state energies and superfluid gaps are calculated for degenerate Fermi systems interacting via long attractive scattering lengths such as cold atomic gases, neutron and nuclear matter. In the intermediate region of densities, where the interparticle spacing $(\sim 1/k_F)$ is longer than the range of the interaction but shorter than the scattering length, the superfluid gaps and the energy per particle are found to be proportional to the Fermi energy and thus differs from the dilute and high density limits. The attractive potential increase linearly with the spin-isospin or hyperspin statistical factor such that, e.g., symmetric nuclear matter undergoes spinodal decomposition and collapses whereas neutron matter and Fermionic atomic gases with two hyperspin states are mechanically stable in the intermediate density region. The regions of spinodal instabilities in the resulting phase diagram are reduced and do not prevent a superfluid transition.Comment: extended and revised version, 7 pages including new phase diagra

The few-body problem for trapped bosons with large scattering length

We calculate energy levels of two and three bosons trapped in a harmonic oscillator potential with oscillator length $a_{\mathrm osc}$. The atoms are assumed to interact through a short-range potential with a scattering length $a$, and the short-distance behavior of the three-body wave function is characterized by a parameter $\theta$. For large positive $a/a_{\mathrm osc}$, the energies of states which, in the absence of the trap, correspond to three free atoms approach values independent of $a$ and $\theta$. For other states the $\theta$ dependence of the energy is strong, but the energy is independent of $a$ for $|a/a_{\mathrm osc}|\gg1$.Comment: 4 pages, 3 figure

Color conductivity and ladder summation in hot QCD

The color conductivity is computed at leading logarithmic order using a Kubo formula. We show how to sum an infinite series of planar ladder diagrams, assuming some approximations based on the dominance of soft scattering processes between hard particles in the plasma. The result agrees with the one obtained previously from a kinetical approach.Comment: 15 pages, 4 figures. Explanations enlarged, two figures and some refs added, typos corrected. Final version to be published in Phys.Rev.