We present simple, concrete, two-fermion models that exhibit thermodynamically stable isotropic translationally-invariant gapless superfluid states (breached pair superfluidity). The mass ratio between the components and the momentum structure of the interaction are crucial for determining the stability of such states: Idealized, momentum-independent ("contact") interactions are insufficient.

We propose a wide universality class of gapless superfluids, and analyze a limit that might be realized in quark matter at intermediate densities. In the breached pairing color superconducting phase heavy s-quarks, with a small Fermi surface, pair with light u or d quarks. The groundstate has a superfluid and a normal Fermi component simultaneously. We expect a second order phase transition, as a function of increasing density, from the breached pairing phase to the conventional color-flavor locked (CFL) phase.Because the primary one-gluon exchange interaction between high-momentum quarks is attractive for quarks in the color antisymmetric3 channel, it is a firm prediction of QCD that cold dense quark matter is a color superconductor. At asymptotic densities (ignoring the c, b and t quarks) the ground state is well understood: quarks of all three flavors u, d, and s, pair according to the BCS mechanism, forming the color-flavor locked (CFL) phase [1].It is much less clear what QCD predicts for the ground state at subasymptotic densities, which could be relevant for describing neutron stars. Differences among the quark masses cause mismatches among the Fermi surfaces of the species which potentially pair. There is no longer an abundance of degenerate low-energy particle-particle or hole-hole states with opposite momenta both near their Fermi surfaces, and so it is less obvious what modes are the best candidates for coherent alignment by attractive interactions.One much-discussed possibility is the LOFF phase (Larkin-Ovchinnikov-Fulde-Ferrel [2]). In the context of QCD these ideas lead to the crystalline color superconductivity [3]. Here we suggest quite a different possibility for ordering with mismatched Fermi surfaces, that might be realized at intermediate densities in QCD.In QCD at intermediate densities, µ ∼ 200 − 300 MeV, there is not only mismatch in quark Fermi surfaces but also a different dispersion relation, since the heavy squark, unlike the light u and d quarks, needs not be ultra-relativistic. This difference makes plausible a pairing phase, wherein strange quarks are raised to higher kinetic energies to exploit favorable possibilities for correlation energy through pairing. The opposite limitpairing of a heavy and light species when heavy species has the larger Fermi surface -is the arena for the interior gap phase discussed in [4].For illustrative purposes we analyze a toy model with a massive s and a massless u quark. The Fermi momenta are related to chemical potentials aswhere δµ e will be tuned to enforce number equality (a stand-in for electric neutrality). We are interested in the case when the Fermi momentum for the s-quark is smaller than that for the u-quark, p s F < p u F . For simplicity, we shall linearize the s quark dispersion near its Fermi surface. We have checked that this simplification does not alter our results qualitatively. Our simplified model then has dispersion relationswith V s < V u . In promoting particles of the heavy species to pair around the large Fermi surface of li...

Candidate homogeneous, isotropic superfluid or superconducting states of paired fermion species with different chemical potentials, can lead to quasiparticle excitation energies that vanish at either zero, one, or two spheres in momentum space. With no zeroes, we have a conventional BCS superconductor. The other two cases, "gapless" superconductors, appear in mean field theory for sufficiently large mismatches and/or sufficiently large coupling strengths. Here we examine several stability criteria for those candidate phases. Positivity of number susceptibility appears to provide the most powerful constraint, and renders all the two-zero states that we have examined mechanically unstable. Our results should apply directly to ultracold fermionic atom systems.

The generalization of the effective action [1] of the quark-antiquark system in the confining vacuum is performed for the case of arbitrary quark masses. The interaction of quarks is described by the averaged Wilson loop for which we use the minimal area law asymptotics.The system is quantized by the path integral method and the quantum Hamiltonian is obtained. It contains not only quark degrees of freedom but also the string energy density.As well as in the equal masses case [1] two dynamical regimes are found [2]: for large orbital excitations (l ≫ 1) the system is represented as rotating string, which leads to asymptotically linear Regge trajectories, while at small l one obtains a potential-like relativistic or nonrelativistic regime.In the limiting cases of light-light and heavy-light mesons a unified description is developed [2]. For the Regge trajectories one obtains nearly straight-line patterns with the slope very close to 1/2πσ and 1/πσ correspondingly. The upper bound on the light quark(s) masses which doesn't change considerably this property of the trajectories is also found. I n t r o d u c t i o nRecently the new approach to study nonperturbative large distance dynamics of quarkantiquark system in the confining vacuum has been developed and the Hamiltonian for the case of equal quark masses has been obtained [1]. In the present paper we consider the general case of arbitrary quark masses. The effective Hamiltonian of the system is derived (for a short report see [2]) and properties of its spectrum are analysed.With the help of vacuum correlator formalizm [3] we represent gauge invariant Green function of the qq system in a form where all dynamics of the interaction is described by the averaged Wilson loop operator. Starting from the QCD Lagrangian and making use of the minimal area 1

A systematic procedure to consistently formulate a field theoretical, QCD bound state problem with a fixed number of constituents is outlined. The approach entails applying the Hamiltonian flow equations, which are a set of continuous unitary transformations, to a QCD motivated Hamiltonian with a confining interaction. The method is developed in detail for gluodynamics in the Coulomb gauge to obtain an effective block-diagonal Hamiltonian appropriate to a reduced Fock space with fixed number of dynamical gluons. Standard many-body techniques are used to numerically diagonalize this Hamiltonian in a constituent two gluon Fock space. The calculated gluon condensates and glueball masses are in good agreement with QCD sum rule and lattice results. PAC number(s):