Phases of a bilayer Fermi gas

We investigate a two-species Fermi gas in which one species is confined in two parallel layers and interacts with the other species in the three-dimensional space by a tunable short-range interaction. Based on the controlled weak coupling analysis and the exact three-body calculation, we show that the system has a rich phase diagram in the plane of the effective scattering length and the layer separation. Resulting phases include an interlayer s-wave pairing, an intralayer p-wave pairing, a dimer Bose-Einstein condensation, and a Fermi gas of stable Efimov-like trimers. Our system provides a widely applicable scheme to induce long-range interlayer correlations in ultracold atoms.Comment: 5 pages, 5 figures; (v2) stability of trimer is emphasized; (v3) published versio

CP-violating theta parameter in the domain model of the QCD vacuum

A non-zero CP-violating $\theta$ parameter is treated in the domain model which assumes a cluster-like vacuum structure whose units are characterised in particular by a topological charge which is not necessarily an integer number. In the present paper we restrict consideration to rational values of the charge. The model has previously been shown to manifest confinement, spontaneous chiral symmetry breaking and the absence of an axial U(1) Goldstone boson. We find that the specific structure of the minima of the free energy density of the domain ensemble forces a $2\pi$-periodicity of observables in $\theta$ for any number of light quarks, that vacuum doubling occurs at $\theta=\pi$ for any $N_f>1$ and any value of topological charge $q$. These features are in agreement with expectations based on anomalous Ward identities and large $N_c$ effective theories. We find also additional values of $\theta$ depending on $q$ for which vacuum doubling occurs.Comment: 10 pages, 6 figures. Final version with modification of Eq.(2), additional references, minor typographical correction

Poincar\'e recurrence theorem and the strong CP-problem

The existence in the physical QCD vacuum of nonzero gluon condensates, such as $$, requires dominance of gluon fields with finite mean action density. This naturally allows any real number value for the unit ``topological charge'' $q$ characterising the fields approximating the gluon configurations which should dominate the QCD partition function. If $q$ is an irrational number then the critical values of the $\theta$ parameter for which CP is spontaneously broken are dense in $\mathbb{R}$, which provides for a mechanism of resolving the strong CP problem simultaneously with a correct implementation of $U_{\rm A}(1)$ symmetry. We present an explicit realisation of this mechanism within a QCD motivated domain model. Some model independent arguments are given that suggest the relevance of this mechanism also to genuine QCD.Comment: 8 pages, RevTeX, 3 figures. Revised after referee suggestions. Now includes model independent argument

Spectral density in resonance region and analytic confinement

We study the role of finite widths of resonances in a nonlocal version of the Wick-Cutkosky model. The spectrum of bound states is known analytically in this model and forms linear Regge tragectories. We compute the widths of resonances, calculate the spectral density in an extension of the Breit-Wigner {\it ansatz} and discuss a mechanism for the damping of unphysical exponential growth of observables at high energy due to finite widths of resonances.Comment: 13 pages, RevTeX, 6 figures. Revised version with typographical corrections and additional comments in conclusion

Impact of the strong electromagnetic field on the QCD effective potential for homogeneous Abelian gluon field configurations

The one-loop quark contribution to the QCD effective potential for the homogeneous Abelian gluon field in the presence of external strong electromagnetic field is evaluated. The structure of extrema of the potential as a function of the angles between chromoelectric, chromomagnetic and electromagnetic fields is analyzed. In this setup, the electromagnetic field is considered as an external one while the gluon field represents domain structured nonperturbative gluon configurations related to the QCD vacuum in the confinement phase. Two particularly interesting gluon configurations, (anti-)self-dual and crossed orthogonal chromomagnetic and chromoelectric fields, are discussed specifically. Within this simplified framework it is shown that the strong electromagnetic fields can play a catalysing role for a deconfinement transition. At the qualitative level, the present consideration can be seen as a highly simplified study of an impact of the electromagnetic fields generated in relativistic heavy ion collisions on the strongly interacting hadronic matter.Comment: 9 pages, 4 figure

On the chirality of quark modes

A model for the QCD vacuum based on a domainlike structured background gluon field with definite duality attributed to the domains has been shown elsewhere to give confinement of static quarks, a reasonable value for the topological susceptibility and indications that chiral symmetry is spontaneously broken. In this paper we study in detail the eigenvalue problem for the Dirac operator in such a gluon mean field. A study of the local chirality parameter shows that the lowest nonzero eigenmodes possess a definite mean chirality correlated with the duality of a given domain. A probability distribution of the local chirality qualitatively reproduces histograms seen in lattice simulations.Comment: RevTeX4, 5 figures, 14 page

Confinement and Chiral Symmetry Breaking via Domain-Like Structures in the QCD Vacuum

A qualitative mechanism for the emergence of domain structured background gluon fields due to singularities in gauge field configurations is considered, and a model displaying a type of mean field approximation to the QCD partition function based on this mechanism is formulated. Estimation of the vacuum parameters (gluon condensate, topological susceptibility, string constant and quark condensate) indicates that domain-like structures lead to an area law for the Wilson loop, nonzero topological susceptibility and spontaneous breakdown of chiral symmetry. Gluon and ghost propagators in the presence of domains are calculated explicitly and their analytical properties are discussed. The Fourier transforms of the propagators are entire functions and thus describe confined dynamical fields.Comment: RevTeX, 48 pages (32 pages + Appendices A-E), new references added [1,2,4,5] and minor formulae corrected for typographical error