Critical Chemical Potential Research Articles

Chiral phase structure of the sixteen meson states in the SU(3) Polyakov linear-sigma model for finite temperature and chemical potential in a strong magnetic field

In characterizing the chiral phase-structure of pseudoscalar ( ), scalar ( ), vector ( ) and axial-vector ( t) meson states and their dependence on temperature, chemical potential, and magnetic field, we utilize the SU(3) Polyakov linear-sigma model (PLSM) in the mean-field approximation. We first determine the chiral (non)strange quark condensates, and , and the corresponding deconfinement order parameters, and , in thermal and dense (finite chemical potential) medium and finite magnetic field. The temperature and the chemical potential characteristics of nonet meson states normalized to the lowest bosonic Matsubara frequency are analyzed. We note that all normalized meson masses become temperature independent at different critical temperatures. We observe that the chiral and deconfinement phase transitions are shifted to lower quasicritical temperatures with increasing chemical potential and magnetic field. Thus, we conclude that the magnetic field seems to have almost the same effect as the chemical potential, especially on accelerating the phase transition, i.e. inverse magnetic catalysis. We also find that increasing the chemical potential enhances the mass degeneracy of the various meson masses, while increasing the magnetic field seems to reduce the critical chemical potential, at which the chiral phase transition takes place. Our mass spectrum calculations agree well with the recent PDG compilations and PNJL, lattice QCD calculations, and QMD/UrQMD simulations.

Structures of the strange quark stars within a quasiparticle model

The structures of strange quark stars are studied within a quasiparticle model obtained by the two-loop approximation. A softer equation of state yields a smaller maximum mass, a smaller radius, and makes the surface energy density and the surface quark chemical potential larger. The parameter space is obtained under the following constraints: the maximum mass of the strange quark star should be larger than 2.0 solar masses, which matches the masses of PSR $\mathrm{J}0348+0432$ and PSR $\mathrm{J}1614\text{\ensuremath{-}}2230$, and the surface energy density should be larger than $2.80\ifmmode\times\else\texttimes\fi{}{10}^{14}\text{ }\text{ }\mathrm{g}/{\mathrm{cm}}^{3}$. In our parameter space, the surface quark chemical potential is smaller than 308 MeV which is the critical quark chemical potential in QCD without electromagnetism. Also, the tidal Love number ${k}_{2}$ and deformability $\mathrm{\ensuremath{\Lambda}}$ are calculated for a 1.4-solar-mass strange quark star. A softer equation of state yields a smaller $\mathrm{\ensuremath{\Lambda}}(1.4)$ and leads to a strange quark star that is more compact and less likely to be tidally deformed. The data of GW170817 indicate that the upper bound of $\mathrm{\ensuremath{\Lambda}}(1.4)$ is 800 for the low-spin prior, which gives an upper bound of the parameter $\ensuremath{\zeta}$ of the running coupling constant ${\ensuremath{\alpha}}_{s}$ and gives a lower bound of the vacuum pressure density $B$, i.e., $\ensuremath{\zeta}l0.098\text{ }\text{ }\mathrm{GeV}$, $Bg(0.111\text{ }\text{ }\mathrm{GeV}{)}^{4}$. Moreover, the constraint on $\ensuremath{\zeta}$ also plays an important role in phenomenological studies of the quark-gluon plasma.

Superconducting Phases in Lithium Decorated Graphene LiC6

A study of possible superconducting phases of graphene has been constructed in detail. A realistic tight binding model, fit to ab initio calculations, accounts for the Li-decoration of graphene with broken lattice symmetry, and includes s and d symmetry Bloch character that influences the gap symmetries that can arise. The resulting seven hybridized Li-C orbitals that support nine possible bond pairing amplitudes. The gap equation is solved for all possible gap symmetries. One band is weakly dispersive near the Fermi energy along Γ → M where its Bloch wave function has linear combination of {d}_{{x}^{2}-{y}^{2}} and dxy character, and is responsible for {d}_{{x}^{2}-{y}^{2}} and dxy pairing with lowest pairing energy in our model. These symmetries almost preserve properties from a two band model of pristine graphene. Another part of this band, along K → Γ, is nearly degenerate with upper s band that favors extended s wave pairing which is not found in two band model. Upon electron doping to a critical chemical potential μ1 = 0.22 eV the pairing potential decreases, then increases until a second critical value μ2 = 1.3 eV at which a phase transition to a distorted s-wave occurs. The distortion of d- or s-wave phases are a consequence of decoration which is not appear in two band pristine model. In the pristine graphene these phases convert to usual d-wave or extended s-wave pairing.

Two Novel Approaches to the Hadron-Quark Mixed Phase in Compact Stars

First-order phase transitions, such as the liquid-gas transition, proceed via formation of structures, such as bubbles and droplets. In strongly interacting compact star matter, at the crust-core transition but also the hadron-quark transition in the core, these structures form different shapes dubbed “pasta phases”. We describe two methods to obtain one-parameter families of hybrid equations of state (EoS) substituting the Maxwell construction that mimic the thermodynamic behaviour of pasta phase in between a low-density hadron and a high-density quark matter phase without explicitly computing geometrical structures. Both methods reproduce the Maxwell construction as a limiting case. The first method replaces the behaviour of pressure against chemical potential in a finite region around the critical pressure of the Maxwell construction by a polynomial interpolation. The second method uses extrapolations of the hadronic and quark matter EoS beyond the Maxwell point to define a mixing of both with weight functions bounded by finite limits around the Maxwell point. We apply both methods to the case of a hybrid EoS with a strong first order transition that entails the formation of a third family of compact stars and the corresponding mass twin phenomenon. For both models, we investigate the robustness of this phenomenon against variation of the single parameter: the pressure increment at the critical chemical potential that quantifies the deviation from the Maxwell construction. We also show sets of results for compact star observables other than mass and radius, namely the moment of inertia and the baryon mass.

Interaction-range effects and universality in the BCS-BEC crossover of spin-orbit–coupled Fermi gases

We explore the evolution of an ultracold quantum gas of interacting fermions crossing from a Bardeen-Cooper-Schrieffer (BCS) superfluidity to a Bose-Einstein condensation (BEC) of molecular bosons in the presence of a tunable-range interaction among the fermions and of an artificial magnetic field, which can be used to simulate a pseudo-spin-orbit coupling (SOC) and to produce topological states. We find that the crossover is affected by a competition between the finite range of the interaction and the SOC and that the threshold for the topological transition is affected by the interactions only in the small pair size, BEC-like, regime. Below , we find persistence of universal behavior in the critical temperature, chemical potential, and condensate fraction, provided that the pair correlation length is used as a driving parameter. Above threshold, universality is lost in the regime of large pair sizes. Here, the limiting ground state departs from a weakly interacting BCS-like one so that a different description is required. Our results can be relevant in view of current experiments with cold atoms in optical cavities, where tunable-range effective atomic interactions can be engineered.

Holographic p-wave superconductor with high-order derivative correction

In the probe limit, we numerically study the holographic p-wave superconductor phase transition in the high-order derivative theory. Concretely, we study the influences of the high-order derivative correction term αRF2 on the Maxwell complex vector model (MCV) in the five-dimensional AdS black hole and soliton backgrounds, respectively. In the black hole background, the improving correction parameter α increases the critical temperature and thus enhances the conductor/superconductor phase transition. Meanwhile, as the RF2 correction becomes stronger, the ratio of the energy gap to the critical temperature decreases from 9.858 to 5.995, which obviously deviates from the universal value. In the soliton background, we find that the correction does not affect the critical chemical potential. However, as the correction parameter α increases, the vector condensate grows faster, which might suggest that the improving α enhances the insulator/superconductor in some sense. The location of the second pole of imaginary part of conductivity increases with α, which implies that the energy of the quasiparticle excitation increases with the improving correction. In addition, the effects of α on the superfluid density agree with the one on the critical value as well as the condensate in both models. Furthermore, the critical exponent of condensate and superfluid density near the critical point is always 1/2 and 1, respectively.

Functional renormalization group study of the quark-meson model with ω meson

We study the phase diagram of two-flavor massless QCD at finite baryon density by applying the functional renormalization group (FRG) for a quark-meson model with $\sigma, \pi$, and $\omega$ mesons. The dynamical fluctuations of quarks, $\sigma$, and $\pi$ are included into the flow equations, while the amplitudes of $\omega$-fields are also allowed to fluctuate. At high temperature the effects of the $\omega$-field on the phase boundary are qualitatively similar to the mean-field calculations; the phase boundary is shifted to the higher chemical potential region. As the temperature is lowered, however, the transition line bends back to the lower chemical potential region, irrespective to the strength of the vector coupling. In our FRG calculations, the driving force of the low temperature first order line is the fluctuations rather the quark density, and the effects of $\omega$-fields have little impact. At low temperature, the effective potential at small $\sigma$ field is very sensitive to the infrared cutoff scale, and this significantly affects our determination of the phase boundaries. The critical chemical potential at the tricritical point is affected by the $\omega$-field effects but its critical temperature stays around the similar value. Some caveats are given in interpreting our model results.

Critical phenomena and chemical potential of a charged AdS black hole

We study the thermodynamics and the chemical potential for a five-dimensional charged AdS black hole by treating the cosmological constant as the number of colors $N$ in the boundary gauge theory and its conjugate quantity as the associated chemical potential $\mu$. It is found that there exists a small-large black hole phase transition. The critical phenomena are investigated in the $N^{2}$-$\mu$ chart. In particular, in the reduced parameter space, all the thermodynamic quantities can be rescaled with the black hole charge such that these reduced quantities are charge-independent. Then we obtain the coexistence curve and the phase diagram. The latent heat is also numerically calculated. Moreover, the heat capacity and the thermodynamic scalar are studied. The result indicates that the information of the first-order black hole phase transition is encoded in the heat capacity and scalar. However, the phase transition point cannot be directly calculated with them. Nevertheless, the critical point linked to a second-order phase transition can be determined by either the heat capacity or the scalar. In addition, we calculate the critical exponents of the heat capacity and the scalar for the saturated small and large black holes near the critical point.

Interplay between chiral symmetry breaking and the QCD Kondo effect

We investigate the interplay between the (light-light quark) chiral condensate and heavy-light quark condensate induced by the QCD Kondo effect, which is described by an effective Lagrangian with four-point interactions and the mean-field approximation. We find that the appearance of Kondo condensates decreases the critical chemical potential of the chiral condensate. In the region near the critical chemical potential, a coexistence phase with two kinds of condensates can appear. The behavior of such an interplay at finite temperature and with nonzero current light-quark mass is also discussed.

On the intra- and interband plasmon modes in doped armchair graphene nanoribbons

With the help of the simple tight-binding Hamiltonian and Green's function technique, we study how intraband and interband plasmon modes of both semiconducting and metallic armchair graphene nanoribbons are influenced by the width, chemical doping, and incident momentum direction. In particular, we investigate the behavior of the frequency-dependent susceptibility when the system is exposed to photons or electrons. Injecting electrons by doping creates a new collective mode due to new states between the valence and conduction bands corresponding to intraband transition for which the effect of ribbon width on these transitions in the semiconducting case is much more sensitive than metallic ones. Furthermore, some critical chemical potential and momentum values for both intraband and interband modes lead to different behaviors for resonant peaks. Another remarkable point is the high sensitivity of intraband plasmons to the direction of incident momentum. In particular, the susceptibility of doped nanoribbons vanishes at perpendicular directions, i.e., the intraband plasmons disappear.

Superfluid density and critical velocity near the Berezinskii-Kosterlitz-Thouless transition in a two-dimensional strongly interacting Fermi gas

We theoretically investigate superfluidity in a strongly interacting Fermi gas confined to two dimensions at finite temperature. Using a Gaussian pair fluctuation theory in the superfluid phase, we calculate the superfluid density and determine the critical temperature and chemical potential at the Berezinskii-Kosterlitz-Thouless transition. We propose that the transition can be unambiguously demonstrated in cold-atom experiments by stirring the superfluid Fermi gas using a red detuned laser beam, to identify the characteristic jump in the local Landau critical velocity at the superfluid-normal interface, as the laser beam moves across the cloud.

Integrability and chemical potential in the (3 + 1)-dimensional Skyrme model

Using a remarkable mapping from the original (3+1)dimensional Skyrme model to the Sine-Gordon model, we construct the first analytic examples of Skyrmions as well as of Skyrmions–anti-Skyrmions bound states within a finite box in 3+1 dimensional flat space-time. An analytic upper bound on the number of these Skyrmions–anti-Skyrmions bound states is derived. We compute the critical isospin chemical potential beyond which these Skyrmions cease to exist. With these tools, we also construct topologically protected time-crystals: time-periodic configurations whose time-dependence is protected by their non-trivial winding number. These are striking realizations of the ideas of Shapere and Wilczek. The critical isospin chemical potential for these time-crystals is determined.

Two-dimensional Bose and Fermi gases beyond weak coupling

Using a formalism based on the two-body S-matrix we study two-dimensional Bose and Fermi gases with both attractive and repulsive interactions. Approximate analytic expressions, valid at weak coupling and beyond, are developed and applied to the Berezinskii–Kosterlitz–Thouless (BKT) transition. We successfully recover the correct logarithmic functional form of the critical chemical potential and density for the Bose gas. For fermions, the BKT critical temperature is calculated in BCS and BEC regimes through consideration of Tan’s contact.

Dimensionally induced one-dimensional to three-dimensional phase transition of the weakly interacting ultracold Bose gas

We investigate the dimensionally induced phase transition from the normal to the Bose-Einstein-condensed phase for a weakly interacting Bose gas in an optical lattice. To this end we make use of the Hartree-Fock-Bogoliubov-Popov theory, where we include numerically exact hopping energies and effective interaction strengths. At first we determine the critical chemical potential, where we find a much better agreement with recent experimental data than a pure Hartree-Fock treatment. This finding originates from an important correction due to quantum fluctuations, which are enhanced in lower dimensions. Furthermore, we determine for the one-dimensional to three-dimensional transition the power-law exponent of the critical temperature for two different noninteracting Bose gas models yielding the same value of 1/2, which indicates that they belong to the same universality class. For the weakly interacting Bose gas we find for both models that this exponent is robust with respect to finite interaction strengths.

Magnetic catalysis of a finite-size pion condensate

We study the Bose-Einstein condensation of a finite size pion gas subject to the influence of a magnetic field. We find the expressions for the critical chemical potential and temperature for the onset of condensation. We show that for values of the external magnetic flux larger than the elemental flux, the critical temperature is larger than the one obtained by considering only finite size effects. We use experimentally reported values of pion source sizes and multiplicities at LHC energies to show that if the magnetic flux, produced initially in peripheral heavy-ion collision, is at least partially preserved up to the hadronic phase, the combined finite size and magnetic field effects give rise to a critical temperature above the kinetic freeze-out temperature. We discuss the implications for the evolution of the pion system created in relativistic heavy-ion collisions.

Holographic study of the QCD matter under external conditions

Holographic QCD is based on the AdS/CFT duality and offers new nonperturbative approaches to understand the strongly interacting regime of gauge theories. One of the primary questions in Quantum Chromodynamics is the clarification of the whole phase diagram of matter out of quarks and gluons as a function of temperature, baryon or quark chemical potential, and other external parameters.We use methods of the bottom-up AdS/QCD approach to bring out the phase structure of several holographic models in which transition to a deconfined phase is related to a (first order) Hawking-Page phase transition. The impact of phenomenological model parameters on the critical temperature and chemical potential is studied in detail. Comparison of the model predictions with results of experimental investigations, lattice QCD simulations and other methods is also done.

A general holographic insulator/superconductor model with dark matter sector away from the probe limit

We investigate holographic phase transitions with dark matter sector in the AdS soliton background away from the probe limit. In cases of weak backreaction, we find that the larger coupling parameter α makes the gap of condensation shallower and the critical chemical potential keeps as a constant. In contrast, for very heavy backreaction, the dark matter sector could affect the critical chemical potential and the order of phase transitions. We also find the jump of the holographic topological entanglement entropy corresponds to a first order transition between superconducting states in this model with dark matter sector. More importantly, for certain sets of parameters, we observe novel phenomenon of retrograde condensation. In a word, the dark matter sector provides richer physics in the phase structure and the holographic superconductor properties are helpful in understanding dark matter.

Condensate flow in holographic models in the presence of dark matter

Holographic model of a three-dimensional current carrying superconductor or superfluid with {\it dark matter} sector described by the additional $U(1)$-gauge field coupled to the ordinary Maxwell one, has been studied in the probe limit. We investigated analytically by the Sturm-Liouville variational method, the holographic s-wave and p-wave models in the background of the AdS soliton as well as five-dimensional AdS black hole spacetimes. The two models of p-wave superfluids were considered, the so called $SU(2)$ and the Maxwell-vector. Special attention has been paid to the dependence of the critical chemical potential and critical transition temperature on the velocity of the condensate and {\it dark matter} parameters. The current $J$ in holographic three-dimensional superconductor studied here, shows the linear dependence on $T_c-T$ for both s and p-wave symmetry. This is in a significant contrast with the previously obtained results for two-dimensional superconductors, which reveal the $(T-T_c)^{3/2}$ temperature dependence. The coupling constant $\alpha$, as well as, chemical potential $\mu_D$ and the velocity $S_D$ of the {\it dark matter}, affect the critical chemical potential of the p-wave holographic $SU(2)$ system. On the other hand, $\alpha$, {\it dark matter} velocity $S_D$ and density $\rho_D$ determine the actual value of the transition temperature of the same superconductor/superfluid set up. However, the {\it dark matter} does not affect the value of the current.

Determination of hadron-quark phase transition line from lattice QCD and two-solar-mass neutron star observations

We aim at drawing the hadron-quark phase transition line in the QCD phase diagram by using the two phase model (TPM) in which the entanglement Polyakov-loop extended Nambu--Jona-Lasinio (EPNJL) model with vector-type four-quark interaction is used for the quark phase and the relativistic mean field (RMF) model is for the hadron phase. Reasonable TPM is constructed by using lattice QCD data and neutron star observations as reliable constraints. For the EPNJL model, we determine the strength of vector-type four-quark interaction at zero quark chemical potential from lattice QCD data on quark number density normalized by its Stefan-Boltzmann limit. For the hadron phase, we consider three RMF models, NL3, TM1 and model proposed by Maruyama, Tatsumi, Endo and Chiba (MTEC). We find that MTEC is most consistent with the neutron star observations and TM1 is the second best. Assuming that the hadron-quark phase transition occurs in the core of neutron star, we explore the density-dependence of vector-type four-quark interaction. Particularly for the critical baryon chemical potential at zero temperature, we determine a range for the quark phase to occur in the core of neutron star.

BEC-BCS crossover in a cold and magnetized two color NJL model

The BEC-BCS crossover for a NJL model with diquark interactions is studied in the presence of an external magnetic field. Particular attention is paid to different regularization schemes used in the literature. A thorough comparison of results is performed for the case of a cold and magnetized two-color NJL model. According to our results, the critical chemical potential for the BEC transition exhibits a clear inverse magnetic catalysis effect for magnetic fields in the range $ 1 \lesssim eB/m_\pi^2 \lesssim 20 $. As for the BEC-BCS crossover, the corresponding critical chemical potential is very weakly sensitive to magnetic fields up to $eB \sim 9\ m_\pi^2$, showing a much smaller inverse magnetic catalysis as compared to the BEC transition, and displays a strong magnetic catalysis from this point on.