At asymptotic high density and low temperature quarks form Cooper pairs in a color-flavor locked (CFL) configuration. The diquark condensates break spontaneously the baryon symmetry, and this fact makes the CFL phase also superfluid. At low temperatures the transport properties are dominated by the contribution of the superfluid phonon, the Goldstone boson associated to baryon symmetry breaking, in full analogy to what happens in superfluid He4. We discuss how to derive transport properties in the ultracold regime making use of an analogue model of gravity. We also review how this model can be used to study the scattering of phonons with quantized vortices in a rotating system. Finally, we consider the implications of these results in studying the rotational properties of compact stars made of CFL quark matter
We find that for large enough strange quark mass, $m_s^2/4 μΔ>2/3(1-0.024),$ kaon condensed CFL phase of asymptotically dense 3 flavor quark matter is unstable with respect to spontaneous generation of currents of Nambu Goldstone bosons due to spontaneous breaking of baryon number symmetry and hypercharge symmetry in CFL$K^0$ ground state. The total baryon and hypercharge currents still vanish in the ground state. We find that CFL$K^0$ and the new state are separated by the first order phase transition.
We compute one of the bulk viscosity coefficients of cold CFL quark matter in the temperature regime where the contribution of mesons, quarks and gluons to transport phenomena is Boltzmann suppressed. In that regime dissipation occurs due to collisions of superfluid phonons, the Goldstone modes associated to the spontaneous breaking of baryon symmetry. We first review the hydrodynamics of relativistic superfluids, and remind that there are at least three bulk viscosity coefficients in these systems. We then compute the bulk viscosity coefficient associated to the normal fluid component of the …
We compute the mean free path and shear viscosity in the color-flavor locked (CFL) phase of dense quark matter at low temperature T, when the contributions of mesons, quarks and gluons to the transport coefficients are Boltzmann suppressed. CFL quark matter displays superfluid properties, and transport phenomena in such cold regime are dominated by phonon-phonon scattering. We study superfluid phonons within thermal field theory and compute the mean free path associated to their most relevant collision processes. Small-angle processes turn out to be more efficient in slowing transport phenomen…
The Ginzburg-Landau equations for magnetic and gluomagnetic gauge fields of the semi-superfluid strings in the color superconducting core of the neutron star with diquark condensate in the color-flavor-locking (CFL) phase are derived. The simultaneous coupling of the CFL diquark condensate to the magnetic and gluomagnetic gauge fields is taken into account. The asymptotic values of these string energies are defined from quantization conditions. It is shown that a lattice of semi-superfluid strings with minimal quantum of circulation emerges in the superconducting quark core during rotation of …
Transport coefficients of dense quark matter are needed to study properties of compact stars. They can tell us about the cooling, vibrational and rotational properties of the star. We report below a computation of the shear viscosity in the CFL phase at low temperature T. CFL quark matter behaves as a superfluid, and at low T its transport properties are dominated by the collisions of superfluid phonons.
We show that topological superfluid strings/vortices with flux tubes exist in the color-flavor locked (CFL) phase of color superconductors. Using a Ginzburg-Landau free energy we find the configurations of these strings. These strings can form during the transition from the normal phase to the CFL phase at the core of very dense stars. We discuss an interesting scenario for a network of strings and its evolution at the core of dense stars.
Superfluid vortices in the color-flavor-locked (CFL) phase of dense quark matter are known to be energetically disfavored relative to well-separated triplets of "semi-superfluid" color flux tubes. However, the short-range interaction (metastable versus unstable) has not been established. In this paper we perform numerical calculations using the effective theory of the condensate field, mapping the regions in the parameter space of coupling constants where the vortices are metastable versus unstable. For the case of zero gauge coupling we analytically identify a candidate for the unstable mode,…
We calculate the bulk viscosity of color-superconducting quark matter in the color-flavor-locked (CFL) phase. We assume that the lightest bosons are the superfluid mode H and the kaons K0 and K+, and that there is no kaon condensate. We calculate the rate of strangeness-equilibrating processes that convert kaons into superfluid modes, and the resultant bulk viscosity. We find that for oscillations with a timescale of milliseconds, at temperatures T << 1 MeV, the CFL bulk viscosity is much less than that of unpaired quark matter, but at higher temperatures the bulk viscosity of CFL matter can b…
At very high densities, QCD is in the color-flavor-locked phase, which is a color-superconducting phase. The diquark condensates break chiral symmetry in the same way as it is broken in vacuum QCD and gives rise to an octet of pseudo-Goldstone bosons and a superfluid mode. The lightest of these are the charged and neutral kaons. For energies below the superconducting gap, the kaons are described by an $O(2)\times O(2)$-symmetric effective scalar field theory with chemical potentials. We use this effective theory to study Bose-condensation of kaons and their properties as functions of the tempe…
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.
The hydrodynamic description of a superfluid is usually based on a two-fluid picture. In this thesis, basic properties of such a relativistic two-fluid system are derived from the underlying microscopic physics of a complex scalar quantum field theory. To obtain analytic results of all non-dissipative hydrodynamic quantities in terms of field theoretic variables, calculations are first carried out in a low-temperature and weak-coupling approximation. In a second step, the 2-particle-irreducible formalism is applied: This formalism allows for a numerical evaluation of the hydrodynamic parameter…
The bulk viscosities of two color-superconducting phases, the color-flavor locked (CFL) phase and the 2SC phase, are computed and compared to the result for unpaired quark matter. In the case of the CFL phase, processes involving kaons and the superfluid mode give the largest contribution to the bulk viscosity since all fermionic modes are gapped. In the case of the 2SC phase, ungapped fermionic modes are present and the process u+d <-> u+s provides the dominant contribution. In both cases, the bulk viscosity can become larger than that of the unpaired phase for sufficiently large temperatures…
We apply Ginzburg-Landau theory to determine BCS pairing in a strongly-coupled uniform superfluid of three-flavor massless quarks in flavor equilibrium. We elucidate the phase diagram near the critical temperature in the space of the parameters characterizing the thermodynamic potential terms of fourth order in the pairing gap. Within the color and flavor antisymmetric channel with zero total angular momentum, the phase diagram contains an isoscalar (IS) color-antitriplet phase and a color-flavor-locked (CFL) phase, reached by a second order transition from the normal state, as well as states …
We calculate the correlation functions needed to describe the linear response of superfluid matter, and go on to calculate the differential cross section for neutral-current neutrino scattering in superfluid neutron matter and in color-flavor locked quark matter (CFL). We report the first calculation of scattering rates that includes neutrino interactions with both pair-breaking excitations and low-lying collective excitations (Goldstone modes). Our results apply both above and below the critical temperature, allowing use in simulations of neutrino transport in supernovae and neutron stars.
We investigate the color-singlet order parameters and the quark description of the Nambu-Goldstone (NG) bosons in the color-flavor locked (CFL) phase. We put emphasis on the NG boson (phason) called ``H'' associated with the $\mathrm{U_B(1)}$ symmetry breaking. We qualitatively argue the nature of H as the second sound in the hydrodynamic regime. We articulate, based on a diquark picture, how the structural change of the condensates and the associated NG bosons occurs continuously from hadronic to CFL quark matter if the quark-hadron continuity is realized. We sharpen the qualitative differenc…
The Hamiltonian formulation of superfluids based on noncanonical Poisson brackets is studied in detail. The assumption that the momentum density is proportional to the flow of the conserved energy is shown to lead to the covariant relativistic theory previously suggested by Khalatnikov, Lebedev and Carter, and some potentials in this theory are given explicitly. We discuss hydrodynamic fluctuations in the presence of dissipative effects and we derive the corresponding set of hydrodynamic correlation functions. Kubo relations for the transport coefficients are obtained.
Starting from low energy effective chiral Lagrangian with gauged Wess-Zumino Witten term, we have derived a hydrodynamic theory for chiral superfluid. It is a non-abelian hydrodynamics at zero temperature with only superfluid components. With an external electromagnetic field and baryonic and axial baryonic chemical potentials turned on, we are able to identify analogs of various anomaly induced term in normal hydrodynamics, including chiral vortical effect, chiral magnetic effect and chiral electric effect. As an example, we solved the hydrodynamic equations for the ground state and observed …
We evaluate the three bulk viscosity coefficients $ζ_1, ζ_2$ and $ζ_3$ in the color-flavor locked (CFL) superfluid phase due to phonons and kaons, which are the lightest modes in that system. We first show that the computation is rather analogous to the computation of the same coefficients in superfluid $^4$He, as due to phonons and rotons. For astrophysical applications, we also find the value of the viscosities when there is a periodic disturbance, and the viscosities also depend on the frequency of the disturbance. In a temperature regime that might be of astrophysical relevance, we find th…
We investigate collective excitations coupled with baryon density in a system of massless three-flavor quarks in the collisionless regime. By using the Nambu-Jona-Lasinio (NJL) model in the mean-field approximation, we derive the spectra both for the normal and color-flavor locked (CFL) superfluid phases at zero temperature. In the normal phase, we obtain zero sound as a low-lying collective mode in the particle-hole (vector) channel. In the CFL phase, when the excitation energy, $ω$, is smaller than the threshold given by twice the pairing gap $Δ$ ($ω<2Δ$), a phonon corresponding to fluctuati…
Color-flavor locked (CFL) quark matter at high densities is a color superconductor, which spontaneously breaks baryon number and chiral symmetry. Its low-energy thermodynamic and transport properties are therefore dominated by the H (superfluid) boson, and the octet of pseudoscalar pseudo-Goldstone bosons of which the neutral kaon is the lightest. We study the CFL-K^0 phase, in which the stress induced by the strange quark mass causes the kaons to condense, and there is an additional ultra-light "K^0" Goldstone boson arising from the spontaneous breaking of isospin. We compute the bulk viscosi…
It has been shown by Son and Surówka that the presence of anomaly in hydrodynamics with global U(1) symmetry can induce vortical and magnetic currents. The induced current is uniquely determined by anomaly from the existence of an entropy current with non-negative divergence. In this work, we extended the analysis to hydrodynamics with U(1) symmetry spontaneously broken, i.e. U(1) superfluid hydrodynamics. We found that all possible first order gradient corrections are determined up to five arbitrary functions, with the entropy current containing one arbitrary function. Furthermore, the stress…
Quark-hadron continuity was proposed as crossover between hadronic matter and quark matter without a phase transition, based on the matching of the symmetry and excitations in both phases. In the limit of a light strange-quark mass, it connects hyperon matter and the color-flavor-locked (CFL) phase exhibiting color superconductivity. Recently, it was proposed that this conjecture could be generalized in the presence of superfluid vortices penetrating both phases (arXiv:1803.05115 [hep-ph]), and it was suggested that one hadronic superfluid vortex in hyperon matter could be connected to one non…
Hydrodynamics of superfluids can be described by formally dividing the fluid into a normal fluid and a superfluid part. In color-flavor locked quark matter, at least one superfluid component is present due to spontaneous breaking of baryon number conservation, and an additional one due to the breaking of strangeness arises once one takes into account kaon condensation. We show how such a two-component description emerges from an underlying scalar field theory which can be viewed as an effective theory for kaons. Furthermore, the occurring hydrodynamic quantities in the low-temperature limit ar…
At very high densities, as for example in the core of a neutron star, matter may appear in the color-flavor locked (CFL) phase, which is a superfluid. This phase features topologically stable vortex solutions, which arise in a spinning superfluid as localized configurations carrying quanta of angular momentum. Despite the topological stability of these vortices they are not the lowest energy state of the system at neutron star densities and decay into triplets of semi-superfluid fluxtubes. In these proceedings we report on the progress of our numerical study in the Ginzburg-Landau approach, wh…
It is well known that the hydrodynamics of a zero-temperature superfluid can be formulated in field-theoretic terms, relating for example the superfluid four-velocity to the gradient of the phase of a Bose-condensed scalar field. At nonzero temperatures, where the phenomenology of a superfluid is usually described within a two-fluid picture, this relationship is less obvious. For the case of a uniform, dissipationless superfluid at small temperatures and weak coupling we discuss this relationship within a phi^4 model. For instance, we compute the entrainment coefficient, which describes the in…
We discuss some low energy properties of color-flavor locked (CFL) superconductors. First, we study how an external magnetic field affects their Goldstone physics in the chiral limit, stressing that there is a long-range component of the field that penetrates the superconductor. We note that the most remarkable effect of the applied field is giving a mass to the charged pions and kaons. By estimating this effect, we see that for values $e B \sim 2 f_πΔ$, where $Δ$ is the quark gap, and $f_π$ the pion decay constant, the charged Goldstone bosons become so heavy, that they turn out to be unstabl…
Extending the quantum effective approach of Son and Nicolis and incorporating dissipation, we develop a MIS formalism for describing a superfluid out of equilibrium by including the Goldstone boson and the condensate together with the hydrodynamic modes as the effective degrees of freedom. We find that the evolution of the superfluid undergoing Bjorken flow is governed by the conventional hydrodynamic attractor with unbroken symmetry and an even number of novel non-dissipative fixed points with broken symmetry. If the initial temperature is super-critical, then the condensate becomes exponenti…
This is a brief report of work performed in arXiv:1106.3576. We consider the chiral transport terms in a relativistic charged superfluid, and their relation to triangle anomalies. The terms allowed by the Second Law of thermodynamics have been worked out. A simplified form is proposed on heuristic grounds, from an analysis of the better-understood chiral effects in normal fluids. We point out the appearance of a "chiral electric conductivity", and relate it through an educated guess to the axial anomaly coefficient.
We study how vortices in dense superfluid hadronic matter can connect to vortices in superfluid quark matter, as in rotating neutron stars, focusing on the extent to which quark-hadron continuity can be maintained. As we show, a singly quantized vortex in three-flavor symmetric hadronic matter can connect smoothly to a singly quantized non-Abelian vortex in three-flavor symmetric quark matter in the color-flavor locked (CFL) phase, without the necessity for boojums appearing at the transition.
Matter at high density and low temperature is expected to be a color superconductor, which is a degenerate Fermi gas of quarks with a condensate of Cooper pairs near the Fermi surface that induces color Meissner effects. At the highest densities, where the QCD coupling is weak, rigorous calculations are possible, and the ground state is a particularly symmetric state, the color-flavor locked (CFL) phase. The CFL phase is a superfluid, an electromagnetic insulator, and breaks chiral symmetry. The effective theory of the low-energy excitations in the CFL phase is known and can be used, even at m…
We argue that turbulence in superfluids is governed by two dimensionless parameters. One of them is the intrinsic parameter q which characterizes the friction forces acting on a vortex moving with respect to the heat bath, with 1/q playing the same role as the Reynolds number Re=UR/νin classical hydrodynamics. It marks the transition between the "laminar" and turbulent regimes of vortex dynamics. The developed turbulence described by Kolmogorov cascade occurs when Re >> 1 in classical hydrodynamics, and q << 1 in the superfluid hydrodynamics. Another parameter of the superfluid turbulence is t…
We present some exact solutions to the ideal hydrodynamics of a relativistic superfluid with an almost-conformal equation of state. The solutions have stress tensors which are invariant under Lorentz boosts in one direction, and represent superfluid generalisations of the Bjorken and Gubser flows. We also study corrections to the flows in first-order hydrodynamics, arguing that dissipation is dominated by the shear viscosity. We present some simple numerical solutions for these viscous corrections. Finally, we estimate the size of corrections to the flows arising when the spontaneously broken …
We analyze the evolution of hydrodynamic fluctuations for QCD matter below $T_c$ in the chiral limit, where the pions (the Goldstone modes) must be treated as additional non-abelian superfluid degrees of freedom, reflecting the broken $SU_L(2) \times SU_R(2)$ symmetry of the theory. In the presence of a finite pion mass $m_π$, the hydrodynamic theory is ordinary hydrodynamics at long distances, and superfluid-like at short distances. The presence of the superfluid degrees of freedom then gives specific contributions to the bulk viscosity, the shear viscosity, and diffusion coefficients of the …
We show how hydrodynamics of relativistic system with broken continuous symmetry can be constructed using the Poisson bracket technique. We illustrate the method on the example of relativistic superfluids.
We argue that the strongly coupled quark-gluon plasma formed at LHC and RHIC can be considered as a chiral superfluid. The "normal" component of the fluid is the thermalized matter in common sense, while the "superfluid" part consists of long wavelength (chiral) fermionic states moving independently. We use the bosonization procedure with a finite cut-off and obtain a dynamical axion-like field out of the chiral fermionic modes. Then we use relativistic hydrodynamics for macroscopic description of the effective theory obtained after the bosonization. Finally, solving the hydrodynamic equations…
We argue that the strongly coupled quark-gluon plasma formed at LHC and RHIC can be considered as a chiral superfluid. The "normal" component of the fluid is the thermalized matter in common sense, while the "superfluid" part consists of long wavelength (chiral) fermionic states moving independently. We use the bosonization procedure with a finite cut-off and obtain a dynamical axion-like field out of the chiral fermionic modes. Then we use relativistic hydrodynamics for macroscopic description of the effective theory obtained after the bosonization. Finally, solving the hydrodynamic equations…
The hydrodynamic description of a superfluid is usually based on a two-fluid picture. We compute the basic properties of the relativistic two-fluid system from the underlying microscopic physics of a relativistic φ^4 complex scalar field theory. We work at nonzero but small temperature and weak coupling, and we neglect dissipation. We clarify the relationship between different formulations of the two-fluid model, and how they are parameterized in terms of partly redundant current and momentum 4-vectors. As an application, we compute the velocities of first and second sound at small temperature…
Rapid new developments have occurred in superfluid hydrodynamics since the discovery of a host of unusual phenomena which arise from the diverse structure and dynamics of quantized vortices in 3He superfluids. These have been studied in rotating flow with NMR measurements which at best provide an accurate mapping of the different types of topological defects in the superfluid order parameter field. Four observations are reviewed here: (1) the interplay of different vortex structures at the first order interface between the two major superfluid 3He phases, 3He-A and 3He-B; (2) the shear flow in…
In this paper we argue that the strongly coupled quark-gluon plasma can be considered as a chiral superfluid. The "normal" component of the fluid is the thermalized matter in common sense, while the "superfluid" part consists of long wavelength (chiral) fermionic states moving independently. We use several nonperturbative techniques to demonstrate that. First, we analyze the fermionic spectrum in the deconfinement phase (Tc < T < 2 Tc) using lattice (overlap) fermions and observe a gap between near-zero modes and the bulk of the spectrum. Second, we use the bosonization procedure with a finite…
