We study the interplay between the chiral and the deconfinement transitions, both at high temperature and high quark chemical potential, by a non local Nambu-Jona Lasinio model with the Polyakov loop in the mean field approximation and requiring neutrality of the ground state. We consider three forms of the effective potential of the Polyakov loop: two of them with a fixed deconfinement scale, cases I and II, and the third one with a µ dependent scale, case III. In the cases I and II, at high chemical potential µ and low temperature T the main contribution to the free energy is due to the Z(3)-neutral three-quark states, mimicking the quarkyonic phase of the large Nc phase diagram. On the other hand in the case III the quarkyonic window is shrunk to a small region. Finally we comment on the relations of these results to lattice studies and on possible common prospects. We also briefly comment on the coexistence of quarkyonic and color superconductive phases.

We present an extensive study on inhomogeneous chiral condensates in QCD at finite density in the chiral limit using a generalized Ginzburg-Landau (GL) approach. Performing analyses on higher harmonics of one-dimensionally (1D) modulated condensates, we numerically confirm the previous claim that the solitonic chiral condensate characterized by Jacobi's elliptic function is the most favorable structure in 1D modulations. We then investigate the possibility of realization of several multidimensional modulations within the same framework. We also study the phase structure far away from the tricritical point by extending the GL functional expanded up to the eighth order in the order parameter and its spatial derivative. On the same basis, we explore a new regime in the extended GL parameter space and find that the Lifshitz point is the point where five critical lines meet at once. In particular, the existence of an intriguing triple point is demonstrated, and its trajectory consists of one of those critical lines.

We investigate the effects of the dynamical formation of the chiral condensates on color superconducting phases under the electric and color neutrality constraints at vanishing temperature. We shall show that the phase appearing next to the color-flavor-locked (CFL) phase down in density depends on the strength of the diquark coupling. In particular, the gapless CFL (gCFL) phase is realized only in a weak coupling regime. We give a qualitative argument on why the gCFL phase in the weak coupling region is replaced by some other phases in the strong coupling, once the competition between dynamical chiral symmetry breaking and the Cooper pair formation is taken into account. 25.75.Nq On the basis of the asymptotic-free nature of QCD and the attraction between quarks due to gluon exchanges, we now believe that the ground state of the quark matter composed of u, d and s quarks at extremely high densities is a special type of color superconducting phases [1,2]; that is the color-flavor locked (CFL) phase where all the quarks equally participate in pairing [3,4].In reality, nature may not, however, allow such an extremely high-density matter to exist, even in the core of neutron stars and in possible quark stars. In such systems at relatively low density corresponding to the quark chemical potential of, say, 500 MeV, the following two ingredients become important for the fate of the CFL phase and determining the pattern of color superconductivities [5,6,7]: Firstly, one can not neglect the effect of the strange quark mass M s which ranges from around 100 MeV to 500 MeV depending on the quark density. Secondly, the constraints of the color and electric neutrality must be satisfied as well as β-equilibrium under the weak interaction. The former causes Fermi-momentum mismatch [8,9,10], and the latter pulls up or down the Fermi momentum of each species of quarks [6,7]; as the density goes lower, the symmetric CFL pairing would cease to be the ground state at some critical density, and some phases other than the CFL phase would appear.One of the recent findings of such novel pairing patterns is the gapless CFL (gCFL) phase [11,12], which is a non-BCS state having some quarks with gapless dispersions despite the same symmetry breaking pattern as the CFL phase. Historically, a possible realization of the stable gapless state was first discussed for the two-flavor color superconducting phase [13]: It was shown that the local charge neutrality gives a so strong constraint that such an exotic state, called the g2SC phase, exists stably; this is in contrast with the case of the electronic superconductivity in metals [14], where the possible gapless state is unstable against the spatial separation into the Pauli-paramagnetic and superconducting phases because of the absence of a long-range force mediated by gauge fields. The gCFL phase is the three flavor analogue of the g2SC phase. Successive detailed studies have revealed a rich phase structure of superconducting quark matter at zero and nonzero temperatures [15,16]. It shoul...

We study the phase structures of charge neutral quark matter under the β-equilibrium for a wide range of the quark-quark coupling strength within a four-Fermion model. A comprehensive and unified picture for the phase transitions from weak to strong coupling is presented. We first develop a technique to deal with the gap equation and neutrality constraints without recourse to numerical derivatives, and show that the off-diagonal color densities automatically vanish with the standard assumption for the diquark condensates. The following are shown by the numerical analyses: (i) The thermally-robustest pairing phase is the two-flavor pairing (2SC) in any coupling case, while the second one for relatively low density is the up-quark pairing (uSC) phase or the color-flavor locked (CFL) phase depending on the coupling strength and the value of strange quark mass. (ii) If the diquark coupling strength is large enough, the phase diagram is much simplified and is free from the instability problems associated with imaginary Meissner masses in the gapless phases. (iii) The interplay between the chiral and diquark dynamics may bring a non-trivial first order transition even in the pairing phases at high density. We confirm (i) also by using the Ginzburg-Landau analysis expanding the pair susceptibilities up to quartic order in the strange quark mass. We obtain the analytic expression for the doubly critical density where the two lines for the second order phase transitions merge, and below which the down-quark pairing (dSC) phase is taken over by the uSC phase. Also we study how the phase transitions from fully gapped states to partially ungapped states are smeared at finite temperature by introducing the order parameters for these transitions.

The character change of a superfluid state due to the variation of the attractive force is investigated in the relativistic framework with a massive fermion. Two crossovers are found. One is a crossover from the usual BCS state to the Bose-Einstein condensation (BEC) of bound fermion pairs. The other is from the BEC to the relativistic Bose-Einstein condensation (RBEC) of nearly massless bound pairs where antiparticles as well as particles dominate the thermodynamics. Possible realization of the BEC and RBEC states in the quark matter is also pointed out. PACS numbers: 74.20.Fg, 03.75.Nt, 11.10.Wx, Recently, new superfluid states in the ultracold gas of fermionic alkali atoms ( 40 K, 6 Li) were realized [1]. Using the Feshbach resonance, the long-standing idea of the crossover from the BCS state to the Bose-Einstein condensation (BEC) [2,3,4] has been extensively examined. The basic concept of the BCS-BEC crossover is as follows: As long as the attractive interaction between fermions is weak, the system exhibits the superfluidity characterized by the energy gap in the BCS mechanism. On the other hand, if the attractive interaction is strong enough, the fermions first form bound molecules (bosons). Then they start to condense into the bosonic zero-mode at some critical temperature. These two situations are smoothly connected without the phase transition.The possible realization of the BCS-BEC crossover in various systems has been theoretically investigated. These include the liquid 3 He [3], the trapped alkali atoms [5], and the nuclear matter [6]. One of the most striking features of the crossover is that the critical temperature in the BEC region is independent of the coupling for the attraction between fermions. This is because the increase of the coupling only affects the internal structure of the bosons, while the critical temperature is determined by the boson's kinetic energy. Thus, the critical temperature reaches a ceiling for the large coupling as long as the binding effect on the boson mass can be neglected. Even in the nuclear matter where the interaction is relatively strong, the binding energy of the deuteron is much smaller than the nucleon mass. This fact allows us to work within a nonrelativistic framework for describing such a crossover.It is interesting to ask how the situation changes in relativistic systems where the binding effect can not be neglected. The color superconducting phase in the dense quark matter [7,8] and the pion superfluid phase at finite isospin density [9] would be examples. In this article, we will show that there could be two crossovers in the relativistic superfluids. One is the ordinary BCS-BEC * E-mail: nishida@nt.phys.s.u-tokyo.ac.jp † E-mail: abuki@yukawa.kyoto-u.ac.jp crossover, where the critical temperature in the BEC region would not plateau because of the relativistic effect. The other is from the BEC state to the novel state, the relativistic BEC (RBEC), where the critical temperature increases to the order of the Fermi energy. In order to explore the BCS-BEC a...