Thermodynamics properties of an interacting system of bosons are considered at finite temperatures and zero chemical potential within the Skyrme-like mean-field model. An interplay between attractive and repulsive interactions is investigated. As a particular example an equilibrium system of pions is discussed. Several modifications of thermodynamic properties in the considered system are found with increasing a strength of attractive forces. Different types of the first order phase transition are classified. Some of these transitions exist also in the Boltzmann approximation. However, effects of the Bose statistics introduce the notable additional changes in the thermodynamic quantities due to a possibility of the Bose-Einstein condensation.
In this proceedings we present a state-of-the-art method of calculating thermodynamic potential at finite temperature and finite chemical potential, using Hard Thermal Loop perturbation theory (HTLpt) up to next-to-next-leading-order (NNLO). The resulting thermodynamic potential enables us to evaluate different thermodynamic quantities including pressure and various quark number susceptibilities (QNS). Comparison between our analytic results for those thermodynamic quantities with the available lattice data shows a good agreement.
We derive the nonextensive thermodynamics of an ideal quantum gas composed by bosons and/or fermions with finite chemical potentials. We find agreement with previous works when $μ\le m$, and some inconsistencies are corrected for fermions when $μ> m$. This formalism is then used to study the thermodynamical properties of hadronic systems based on a Hadron Resonance Gas approach. We apply this result to study the protoneutron star stability under several conditions.
We present in this work a generalization of the solution of Gorenstein and Yang to the inconsistency problem of thermodynamics for systems of quasi-particles whose masses depend on both the temperature and the chemical potential. We work out several solutions for an interacting system of quarks and gluons and show that there is only one type of solution that reproduce both perturbative and lattice QCD.
The non extensive thermodynamics of an ideal gas composed by bosons and/or fermions is derived from its partition function for systems with finite chemical potentials. It is shown that the thermodynamical quantities derived in the present work are in agreement with those obtained in previous works when $μ\le m$. However some inconsistencies of previous references are corrected when $μ> m$. A discontinuity in the first derivatives of the partition function and its effects are discussed in detail. We show that at similar conditions, the non extensive statistics provide a harder equation of state…
The QCD transition from a hadronic to a quark-gluon plasma phase is a cross-over at vanishing/small baryo-chemical potential, while at higher chemical potentials it is argued that it becomes of first order, ending with a critical end-point. The present goal is the determination of the critical line and, possibly, the recognition of the critical endpoint. For this purpose, the effective model (Nambu-Jona-Lasinio model with Polyakov Loop) with 2+1 flavours is used. In Mean Field Approximation it is possible to obtain all thermodynamic quantities (pressure, entropy, energy and quark density) and …
We extend our work on QCD thermodynamics with 2+1 quark flavors at nonzero chemical potential to finer lattices with $N_t=6$. We study the equation of state and other thermodynamic quantities, such as quark number densities and susceptibilities, and compare them with our previous results at $N_t=4$. We also calculate the effects of the addition of the charm and bottom quarks on the equation of state at zero and nonzero chemical potential. These effects are important for cosmological studies of the early Universe.
We calculate the three-loop thermodynamic potential of QCD at finite temperature and chemical potential(s) using the hard-thermal-loop perturbation theory (HTLpt) reorganization of finite temperature and density QCD. The resulting analytic thermodynamic potential allows us to compute the pressure, energy density, and entropy density of the quark-gluon plasma. Using these we calculate the trace anomaly, speed of sound, and second-, fourth-, and sixth-order quark number susceptibilities. For all observables considered we find good agreement between our three-loop HTLpt calculations and available…
An effective quasiparticle description of the thermodynamics of deconfined matter, compatible with both finite-temperature lattice data and the perturbative limit, is generalized to finite chemical potential. Within this approach, the available 4-flavor lattice equation of state is extended to finite baryon density, and implications for cold, charge-neutral deconfined matter in beta-equilibrium in compact stars are considered.
We review the existing weak-coupling results on the thermodynamic potential of deconfined QCD at small and large quark chemical potential and compare with results from lattice gauge theory as well as the exactly solvable case of large-N_f QCD. We also discuss the new analytical results on non-Fermi-liquid effects in entropy and specific heat as well as in dispersion laws of quark quasiparticles at large quark chemical potential.
We present large $N_f$ QCD/QED as a test bed for improved pressure calculations, show how to apply the hints obtained on optimized renormalization scales at large $N_f$ to finite $N_f=2$, and compare the results to recent lattice data.
Based on the q-deformed oscillator algebra, we study the behavior of the mean occupation number and its analogies with intermediate statistics and we obtain an expression in terms of an infinite continued fraction, thus clarifying successive approximations. In this framework, we study the thermostatistics of q-deformed bosons and fermions and show that thermodynamics can be built on the formalism of q-calculus. The entire structure of thermodynamics is preserved if ordinary derivatives are replaced by the use of an appropriate Jackson derivative and q-integral. Moreover, we derive the most imp…
When the spontaneous symmetry breaking occurs for systems without Lorentz covariance, there arises possible mismatch, $N_{\rm NG} < N_{\rm BG}$, between numbers of Nambu-Goldstone (NG) bosons ($N_{\rm NG}$) and the numbers of broken generators ($N_{\rm BG}$. In such a situation, so-called type-II NG bosons emerge. We study how the gauge bosons acquire masses through the Higgs mechanism under this mismatch by employing gauge theories with complex scalar field at finite chemical potential and by enforcing "charge" neutrality. To separate the physical spectra from unphysical ones, the $R_ξ$ gauge…
We study the thermostatistics of q-deformed bosons and fermions obeying the symmetric algebra and show that it can be built on the formalism of q-calculus. The entire structure of thermodynamics is preserved if ordinary derivatives are replaced by an appropriate Jackson derivative. In this framework, we derive the most important thermodynamic functions describing the q-boson and q-fermion ideal gases in the thermodynamic limit. We also investigate the semi-classical limit and the low temperature regime and demonstrate that the nature of the q-deformation gives rise to pure quantum statistical …
We explore the quasiparticle model at finite chemical potential related to Ru-Keng Su's distinguished contributions to the topic. Besides, we discuss recent developments in the model, and in particular, one argues that the effective mass of the quasiparticle might attain a specific form as a function of momentum, in addition to its dependence on temperature and chemical potential. Unlike the approaches based on the properties of underlying symmetry or renormalization group, the momentum dependence emerges as a special solution to an integro-differential equation resulting from the underlying t…
We study the electroweak standard model at finite temperature in presence of a bosonic chemical potential associated with the conserved electromagnetic current. To preserve the thermodynamic equilibrium of the system, the thermal medium is neutralized by the introduction of four background charges related to the four gauge bosons of this model. Using the mean-field approximation, in the high temperature limit, we find that there exists a difference between the effective mass of the spatial and temporal components of the W boson. A W boson condensation induced via the background charges allows …
Using the method of locally equilibrium statistical operator we consider the thermalized relativistic quantum fields in an oscillatory trap. We compare this thermal picture of the confined boson gas with non-relativistic model of independent factorized sources. We find that they are equivalent in the limit of very large effective sizes $R$, more exactly, when the Compton wave length $1/m$ and thermal wave length $1/\sqrt{% mT}$ are much smaller than {\}$R$ . Under this conditions we study the influence of Bose condensation in finite volumes on the structure of the Wigner function, momentum spe…
We analyze the effects of finite chemical potential on spontaneous breaking of internal symmetries within the class of relativistic field theories described by the linear sigma model. Special attention is paid to the emergence of ``abnormal'' Goldstone bosons with quadratic dispersion relation. We show that their presence is tightly connected to nonzero density of the Noether charges, and formulate a general counting rule. The general results are demonstrated on an SU(3)xU(1) invariant model with an SU(3)-sextet scalar field, which describes one of the color-superconducting phases of QCD.
In this lecture we compare different QCD-like partition functions with bosonic quarks and fermionic quarks at nonzero chemical potential. Although it is not a surprise that the ground state properties of a fermionic quantum system and a bosonic quantum system are completely different, the behavior of partition functions with bosonic quarks does not follow our naive expectation. Among other surprises, we find that the partition function with one bosonic quark only exists at nonzero chemical potential if a conjugate bosonic quark and a conjugate fermionic quark are added to the partition functio…
We study the properties of a star made of self-gravitating bosons gas in a mean-field approximation. A generalized set of Tolman-Oppenheimer-Volkov(TOV) equations is derived to incorporate the effect of chemical-potential in the general relativistic frame work. The metric-dependence of the chemical-potential gives a new class of solutions for the boson stars. It is demonstrated that the maximum mass and radius of the star change in a significant way when the effect of finite chemical-potential is considered. We also discuss the case of a boson star made of quark-condensates. It is found that w…
Based on the constituent quasiparticle model of the quark-gluon plasma (QGP), color quantum path-integral Monte-Carlo (PIMC) calculations of the thermodynamic properties of the QGP are performed. We extend our previous zero chemical potential simulations to the QGP at finite baryon chemical potential. The results indicate that color PIMC can be applied not only above the QCD critical temperature $T_c$ but also below $T_c$. Besides reproducing the lattice equation of state our approach yields also valuable additional insight into the internal structure of the QGP, via the pair distribution func…
The thermodynamical properties of a neutral vector boson gas in a constant magnetic field are studied starting from the spectrum given by Proca formalism. Bose Einstein Condensation (BEC) and magnetization are obtained, for the three and one dimensional cases, in the limit of low temperatures. In three dimensions the gas undergoes a phase transition to an usual BEC in which the critical temperature depends on the magnetic field. In one dimension a diffuse condensate appears as for the charged vector boson gas. In both cases, the condensation is reached not only by decreasing the temperature bu…
In a previous paper (JHEP {\bf 05} (2014) 27), we calculated the three-loop thermodynamic potential of QCD at finite temperature $T$ and quark chemical potentials $μ_q$ using the hard-thermal-loop perturbation theory (HTLpt) reorganization of finite temperature and density QCD. The result allows us to study the thermodynamics of QCD at finite temperature and isospin chemical potential $μ_I$. We calculate the pressure, energy density, and entropy density, the trace anomaly, and the speed of sound at zero and nonzero $μ_I$. The second, fourth, and sixth-order isospin susceptibilities are calcula…
We present a derivation of an exact high temperature expansion for a one-loop thermodynamic potential $Ω(\tildeμ)$ with complex chemical potential $\tildeμ$. The result is given in terms of a single sum the coefficients of which are analytical functions of $\tildeμ$ consisting of polynomials and polygamma functions, decoupled from the physical expansion parameter $βm$. The analytic structure of the coefficients permits us to explicitly calculate the thermodynamic potential for the imaginary chemical potential and analytically continue the domain to the complex $\tildeμ$ plane. Furthermore, our…
We compare recent lattice studies of QCD thermodynamics at non-zero quark chemical potential with the thermodynamics of a hadron resonance gas. We argue that for T < Tc the equation of state derived from Monte--Carlo simulations of two flavour QCD at non-zero chemical potential can be well described by a hadron resonance gas when using the same set of approximations as used in current lattice calculations. We estimate the importance of truncation errors arising from the use of a Taylor expansion in terms of the quark chemical potential and examine the influence of unphysically large quark mass…
By using a simple thermodynamical method we confirm the finding of Chavanis and Harko that stable Bose-Einstein condensate stars can form. However, by using a thermodynamically consistent boson equation of state, we obtain a less massive Bose-Einstein condensate star compared to the one predicted by Chavanis and Harko. We also obtain that the maximum mass of a boson star is insensitive to the change of matter temperature. However, the mass of boson star with relatively large radius depends significantly on the temperature of the boson matter.
We study the thermodynamics of the 2+1 dimensional Gross-Neveu model in the presence of a chemical potential by introducing a representation for the canonical partition function which encodes both real and imaginary chemical potential cases. It is pointed out that the latter case probes the thermodynamics of the possible anyon-like excitations in the spectrum. It is also intimately connected to the breaking of the discrete Z-symmetry of a U(1) gauge theory coupled to the Gross-Neveu model at finite temperature, which we interpret as signaling anyon deconfinement. Finally, the chiral properties…
We investigate two-flavour and two-colour QCD at finite temperature and chemical potential in comparison with a corresponding Nambu and Jona-Lasinio model. By minimizing the thermodynamic potential of the system, we confirm that a second order phase transition occurs at a value of the chemical potential equal to half the mass of the chiral Goldstone mode. For chemical potentials beyond this value the scalar diquarks undergo Bose condensation and the diquark condensate is nonzero. We evaluate the behaviour of the chiral condensate, the diquark condensate, the baryon charge density and the masse…
We discuss the isentropic trajectories on the QCD phase diagram in the temperature and the quark chemical potential plane using the Nambu--Jona-Lasinio model with the Polyakov loop coupling (PNJL model). We impose a constraint on the strange quark chemical potential so that the strange quark density is zero, which is the case in the ultra relativistic heavy-ion collisions. We compare our numerical results with the truncated estimates by the Taylor expansion in terms of the chemical potential to quantify the reliability of the expansion used in the lattice QCD simulation. We finally discuss the…
We consider an interacting pion gas in the regime where thermal but not chemical equilibrium has been reached. Approximate particle number conservation is implemented by a nonvanishing pion chemical potential $μ_π$ within a diagrammatic thermal field theory approach, valid in principle for any bosonic field theory in this regime. The resulting Feynman rules are then applied within the context of Chiral Perturbation Theory to discuss thermodynamical quantities of interest for the pion gas such as the free energy, the quark condensate and thermal self-energy. In particular, we derive the $μ_π\ne…
Thermodynamics of magnetized BPS baryonic layers and the effects of the Isospin chemical potential
Università dell’Insubria（因苏布里亚大学）；INFN sezione di Milano（意大利国家核物理研究所米兰分部）；Como Lake centre for AstroPhysics (CLAP)（科莫湖天体物理中心）；Centro de Estudios Científicos (CECs)（科学研究中心）；Universidad San Sebastián（圣塞巴斯蒂安大学）；Universidad de Concepción（孔塞普西翁大学）；Universitá di Milano Bicocca（米兰比可卡大学）；Gruppo Nazionale di Fisica Matematica, InDAM（数学物理全国小组，印度姆）；Università di Napoli Federico II（那不勒斯费德里科二世大学）；INFN, Sezione di Napoli（意大利国家核物理研究所那不勒斯分部）
We study QCD thermodynamics in presence of two independent imaginary chemical potentials coupled to two degenerate flavors of staggered quarks. Analytic continuation is used to determine non-linear susceptibilities, to test the Hadron Resonance Gas (HRG) model below the zero density critical temperature, Tc, and to determine the average phase factor of the fermion determinant. Deviations from HRG predictions, of the order of a few percent, are clearly visible for temperatures T > 0.95 Tc. The determination of non-linear susceptibilities, using different interpolating functions for analytic con…
We study the thermodynamics of the two flavor massless Schwinger model on a torus at a finite chemical potential. We show that thermodynamic quantities only depend on the isospin chemical potential and there are marked deviations from a free fermion theory.
We summarize the derivation of the finite temperature, finite chemical potential thermodynamic potential in the bag-model approximation to quantum chromodynamics (QCD) that includes a finite $s$-quark mass in the Feynman diagram contributions for both zero-order and two-loop corrections to the quark interaction. The thermodynamic potential for quarks in QCD is a desired ingredient for computations of the equation of state in the early universe, supernovae, neutron stars, and heavy-ion collisions. The 2-loop contributions are normally divergent and become even more difficult in the limit of fin…
The issue discussed is a thermodynamic version of the Bern-Kosower master amplitude formula, which contains all necessary one-loop Feynman diagrams. It is demonstrated how the master amplitude at finite values of temperature and chemical potential can be formulated within the framework of the world-line formalism. In particular we present an elegant method how to introduce a chemical potential for a loop in the master formula. Various useful integral formulae for the master amplitude are then obtained. The non-analytic property of the master formula is also derived in the zero temperature limi…
We discuss an effective Polyakov loop model for QCD thermodynamics with a chemical potential. Using high temperature expansion techniques the partition sum is mapped exactly onto the partition sum of a flux model. In the flux representation the complex action problem is resolved and a simulation with worm-type algorithms becomes possible also at finite chemical potential.
