Fermionic superfluids : from cold atoms to high density QCD : gapless (breached pair) superfluidity and kaon condensation

Abstract

In this thesis, we explore aspects of fermionic superfluidity through a mean-field approximation. Our framework is extremely general, includes both pairing and Hartree-Fock contributions, and is derived rigorously from a variational principle. This framework allows us to analyze a wide range of fermionic systems. In this thesis, we shall consider two-species nonrelativistic atomic systems with various types of interactions, and relativistic QCD systems with 3 x 3 x 4 = 36 different quark degrees of freedom (3 colours, 3 flavours, and 4 relativistic degrees of freedom). We discuss properties of a new state of matter: gapless (Breached Pair) superfluidity, and include a summary of potential experimental realizations. We also present numerical results for a completely self-consistent approximation to the NJL model of high-density QCD and use these results to demonstrate a microscopic realization of kaon condensation. We describe how to match the mean-field approximation to the low-energy chiral effective theory of pseudo-Goldstone bosons, and we extract the numerical coefficients of the lowest order effective potential.