We derive a formula that defines quantum fluctuations of energy in subsystems of a hot relativistic gas. For small subsystem sizes we find substantial increase of fluctuations compared to those known from standard thermodynamic considerations. However, if the size of the subsystem is sufficiently large, we reproduce the result for energy fluctuations in the canonical ensemble. Our results are subsequently used in the context of relativistic heavy-ion collisions to introduce limitations of the concepts such as classical energy density or fluid element. In the straightforward way, our formula can be applied in other fields of physics, wherever one deals with hot and relativistic matter.
Quantum features of the baryon number fluctuations in subsystems of a hot and dense relativistic gas of fermions are analyzed. We find that the fluctuations in small systems are significantly increased compared to their values known from the statistical physics, and diverge in the limit where the system size goes to zero. The numerical results obtained for a broad range of the thermodynamic parameters expected in heavy-ion collisions are presented. They can be helpful to interpret and shed new light on the experimental data.
Explicit expressions for quantum fluctuations of energy in subsystems of a hot relativistic gas of spin-$1/2$ particles are derived. The results depend on the form of the energy-momentum tensor used in the calculations, which is a feature described as pseudo-gauge dependence. However, for sufficiently large subsystems the results obtained in different pseudo-gauges converge and agree with the canonical-ensemble formula known from statistical physics. As different forms of the energy-momentum tensor of a gas are a priori equivalent, our finding suggests that the concept of quantum fluctuations …
We present a simple calculation of the nucleon self-energy in nuclear matter at finite temperature in a relativistic framework, using the real time thermal field theory. The imaginary parts of one-loop graphs are identified with discontinuities across the unitary and the Landau cuts. We find that in general both the cuts contribute significantly to the spectral function in the region of (virtual) nucleon mass usually considered, even though the unitary cut is ignored in the literature. Also our relativistic spectral function differs from the one in non-relativistic approximation, used in some …
We find the equation of state $p,ρ\propto T^6,$ which gives the value of the sound velocity $c^2=0.20,$ in agreement with the ``realistic'' equation of state for hot hadronic matter suggested by Shuryak, in the framework of a covariant relativistic statistical mechanics of an event--anti-event system with small chemical and mass potentials. The relativistic mass distribution for such a system is obtained and shown to be a good candidate for fitting hadronic resonances, in agreement with the phenomenological models of Hagedorn, Shuryak, {\it et al.} This distribution provides a correction to th…
By solving two body Dirac equations with potentials at finite temperature, we calculated the dissociation temperature T_d of B_c mesons in the quark-gluon plasma. It is found that the T_d becomes higher with the relativistic correction than the T_d from the Schroedinger equation. Both the short range interaction and the constant term of the potential at the long-range scale have a contribution to the shift of T_d, while the spin interaction is negligible.
We review the progress achieved in extracting the properties of hot and dense matter from relativistic heavy ion collisions at the relativistic heavy ion collider (RHIC) at Brookhaven National Laboratory and the large hadron collider (LHC) at CERN. We focus on bulk properties of the medium, in particular the evidence for thermalization, aspects of the equation of state, transport properties, as well as fluctuations and correlations. We also discuss the in-medium properties of hadrons with light and heavy quarks, and measurements of dileptons and quarkonia. This review is dedicated to the memor…
A full (3+1)-dimensional calculation using the Lagrangian hydrodynamics is proposed for relativistic nuclear collisions. The calculation enables us to evaluate anisotropic flow of hadronic matter which appears in non-central and/or asymmetrical relativistic nuclear collisions. Applying hydrodynamical calculations to the deformed uranium collisions at AGS energy region, we discuss the nature of space-time structure and particle distributions in detail.
The second-order hydrodynamic equations for evolution of shear and bulk viscous pressure have been derived within the framework of covariant kinetic theory based on the effective fugacity quasiparticle model. The temperature-dependent fugacity parameter in the equilibrium distribution function leads to a mean field term in the Boltzmann equation which affects the interactions in the hot QCD matter. The viscous corrections to distribution function, up to second-order in gradient expansion, have been obtained by employing a Chapman-Enskog like iterative solution of the effective Boltzmann equati…
The parameters obtained from the theoretical analysis of the single photon spectra observed by the WA98 collaboration at SPS energies have been used to evaluate the two photon correlation functions. The single photon spectra and the two photon correlations at RHIC energies have also been evaluated, taking into account the effects of the possible spectral change of hadrons in a thermal bath. We find that the ratio $R_{side}/R_{out} \sim 1$ for SPS and $R_{side}/R_{out} <1$ for RHIC energy.
Based on a hydrodynamical model, we compare 130 GeV/$A$ Au+Au collisions at RHIC and 17 GeV/$A$ Pb+Pb collisions at SPS. The model well reproduces the single-particle distributions of both RHIC and SPS. The numerical solution indicates that huge amount of collision energy in RHIC is mainly used to produce a large extent of hot fluid rather than to make a high temperature matter; longitudinal extent of the hot fluid in RHIC is much larger than that of SPS and initial energy density of the fluid is only 5% higher than the one in SPS. The solution well describes the HBT radii at SPS energy but sh…
This lecture presents an overview of the status of the investigation of the properties of the quark-gluon plasma using relativistic heavy ion collisions at the Relativistic Heavy Ion Collider (RHIC) and the Large Hadron Collider (LHC). It focuses on the insights that have been obtained by the comparison between experimental data from both facilities and theoretical calculations.
We study two recently proposed equations of state (EOS) which are obtained from high temperature QCD, and show how they can be adapted to use them for making predictions for relativistic heavy ion collisions. The method involves extracting equilibrium distribution functions for quarks and gluons from the EOS, which in turn will allow a determination of the transport and other bulk properties of the quark gluon plasma. Simultaneously, the method also yields a quasi particle description of interacting quarks and gluons. The first EOS is perturbative in the QCD coupling constant and has contribut…
Despite the fact that a system created in relativistic heavy ion collisions is an isolated quantum system, which cannot increase its entropy in the course of unitary quantum evolution, hydrodynamical analysis of experimental data seems to indicate that the matter formed in the collisions is thermalized very quickly. Based on common consideration of hydrodynamics as an effective theory in the domain of slow- and long-length modes, we discuss the physical mechanisms responsible for the decoherence and emergence of the hydrodynamic behavior in such collisions, and demonstrate how such physical me…
A formula to calculate the quantum fluctuations of energy in small subsystems of a hot and relativistic gas is derived. We find an increase in fluctuations for subsystems of small sizes, but we agrees with the energy fluctuations in the canonical ensemble if the size is large enough. Not only one can use our expression to find the limit of the concepts of energy density or fluid element in connection to relativistic heavy-ion collisions, but also in other areas of physics where one studies matter with high temperature and velocity.
Non-ideal fluid dynamics with cylindrical symmetry in transverse direction and longitudinal scaling flow is employed to simulate the space-time evolution of the quark-gluon plasma produced in heavy-ion collisions at RHIC energies. The dynamical expansion is studied as a function of initial energy density and initial time. A causal theory of dissipative fluid dynamics is used instead of the standard theories which are acausal. We compute the parton momentum spectra and HBT radii from two-particle correlation functions. We find that, in non-ideal fluid dynamics, the reduction of the longitudinal…
We present recent results on bulk observables and electromagnetic probes obtained using a hybrid approach based on the Ultrarelativistic Quantum Molecular Dynamics transport model with an intermediate hydrodynamic stage for the description of heavy-ion collisions at AGS, SPS and RHIC energies. After briefly reviewing the main results for particle multiplicities, elliptic flow, transverse momentum and rapidity spectra, we focus on photon and dilepton emission from hot and dense hadronic matter.
A recently proposed method for the characterization and analysis of local equilibrium states in relativistic quantum field theory is applied to a simple model. Within this model states are identified which are locally (but not globally) in thermal equilibrium and it is shown that their local thermal properties evolve according to macroscopic equations. The largest space-time regions in which local equilibrium states can exist are timelike cones. Thus, although the model does not describe dissipative effects, such states fix in a natural manner a time direction. Moreover, generically they deter…
In the fractional nonrelativistic potential model, the decomposition of heavy quarkonium in a hot magnetized medium is investigated. The analytical solution of the fractional radial Schrodinger equation for the hot-magnetized interaction potential is displayed by using the conformable fractional Nikiforov-Uvarov method. Analytical expressions for the energy eigenvalues and the radial wave function are obtained for arbitrary quantum numbers. Next, we study the charmonium and bottmonium binding energies for different magnetic field values in the thermal medium. The effect of the fractional param…
In this paper, quarkonium dissociation is investigated in an anisotropic plasma in the hot and dense media. For that purpose, the multidimensional Schrodinger equation is solved analytically by Nikiforov-Uvarov (NU) method for the real part of the potential in an anisotropic medium. The binding energy and dissociation temperature are calculated. In comparison with an isotropic medium, the binding energy of quarkonium is enhanced in the presence of an anisotropic medium. The present results show that the dissociation temperature increases with increasing anisotropic parameter for 1S state of th…
The early stage of high multiplicity nuclear collisions is represented by a nearly quarkless, hot, deconfined pure gluon plasma. This new scenario should be characterized by a suppression of high $p_T$ photons and dileptons as well as by reduced baryon to meson ratios. We present the numerical results for central Pb+Pb collisions at the LHC energies by using the ideal Bjorken hydrodynamics with time-dependent quark fugacity. It is shown that about 25\% of final total entropy is generated during the hydrodynamic evolution of chemically undersaturated quark-gluon plasma.
This presents an overview of relativistic hydrodynamic modeling in heavy-ion collisions prepared for Hot Quarks 2016, at South Padre Island, TX, USA. The influence of the initial state and viscosity on various experimental observables are discussed. Specific problems that arise in the hydrodynamical modeling at the Beam Energy Scan are briefly discussed.
We propose a new kind of two-particle correlation of identified hadrons in longitudinal rapidity space, called $G_{αβ}(y_α,y_β)$, which can reflect clearly the charge correlations of hot quark system produced in AA collisions at LHC energies. It is derived from the basic scenario of quark combination mechanism of hadron production. Like the elliptic flow of identified hadrons at intermediate transverse momentum, this correlation is independent of the absolute hadronic yields but dependent only on the flavor compositions of hadrons, and thus exhibits interesting properties for different kinds o…
We introduce a combined macroscopic/microscopic transport approach employing relativistic hydrodynamics for the early, dense, deconfined stage of the reaction and a microscopic non-equilibrium model for the later hadronic stage where the equilibrium assumptions are not valid anymore. Within this approach we study the dynamics of hot, bulk QCD matter, which is expected to be created in ultra-relativistic heavy ion collisions at the SPS, the RHIC and the LHC. Our approach is capable of self-consistently calculating the freeze-out of the hadronic system, while accounting for the collective flow o…
Within the context of relativistic nuclear collisions aimed at exploring hot and baryon-dense matter, we investigate how the general features of the expansion dynamics, as well as a number of specific observables, depend on the equation of state used in dynamical simulations of the non-equilibrium confinement phase transition.
The possibility of pion--pair formation in a hot pion gas, based on the bosonic gap equation, is pointed out and discussed in detail. The critical temperature for condensation of pion pairs (Evans--Rashid transition) is determined as a function of the pion density. As for fermions, this phase transition is signaled by the appearance of a pole in the two--particle propagator. In bose systems there exists a second, lower critical temperature, associated with the appearance of the single--particle condensate. Between the two critical temperatures the pion dispersion relation changes from the usua…
We have explored the multi-component structure of electrical conductivity of relativistic Fermionic and Bosonic fluid in presence of magnetic field by using Kubo approach. This is done by explicitly evaluating the thermo-magnetic vector current spectral functions using the real time formalism of finite temperature field theory and the Schwinger proper time formalism. In absence of magnetic field, the one-loop diagramatic representation of Kubo expression of any transport coefficients is exactly same with relaxation time approximation (RTA) based expression, but this equality does not hold for …
The adaptation of Wigner's induced representation for a relativistic quantum theory making possible the construction of wavepackets and admitting covariant expectation values for the coordinate operator x^μintroduces a foliation on the Hilbert space of states. The spin-statistics relation for fermions and bosons implies the universality of the parametrization of orbits of the induced representation, implying that all particles within the identical particle sets transform under the same SU(2) subgroup of the Lorentz group, and therefore their spins and angular momentum states can be computed us…
Jet-quenching and photon production at high transverse momentum are studied at RHIC energies, together with the correlation between jets and photons. The energy loss of hard partons traversing the hot QGP is evaluated in the AMY formalism, consistently taking into account both induced gluon emission and elastic collisions. The production of high $p_T$ photons in Au+Au collisions is calculated, incorporating a complete set of photon-production channels. Putting all these ingredients together with a (3+1)-dimensional ideal relativistic hydrodynamical description of the thermal medium, we achieve…
The expansion dynamics of hot electron-positron-photon plasma droplets is dealt with within relativistic hydrodynamics. Such droplets, envisaged to be created in future experiments by irradiating thin foils with counter-propagating ultra-intense laser beams, are sources of flashes of gamma radiation. Warm electron-positron plasma droplets may be identified and characterized by a broadened 511 keV line.
