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Register a new userPseudo-gauge dependence of quantum fluctuations of energy in a hot relativistic gas of fermions
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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 of energy in very small thermodynamic systems is pseudo-gauge dependent. On the practical side, the results of our calculations determine a scale of coarse graining for which the choice of the pseudo-gauge becomes irrelevant.
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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.
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.
Two-particle angular correlation for charged particles emitted in Au+Au collisions at the center-of-mass of 200 MeV measured at RHIC energies revealed novel structures commonly referred to as a near-side ridge. The ridge phenomenon in relativistic A+A collisions is rooted probably in the initial conditions of the thermal evolution of the system. In this study we analyze the evolution of the bumping transverse structure of the energy density distribution caused by fluctuations of the initial density distributions that could lead to the ridge structures. We suppose that at very initial stage of collisions the typical one-event structure of the initial energy density profile can be presented as the set of longitudinal tubes, which are boost-invariant in some space-rapidity region and are rather thin. These tubes have very high energy density comparing to smooth background density distribution. The transverse velocity and energy density profiles at different times of the evolution till the chemical freeze-out (at the temperature T=165 MeV) willbe reached by the system are calculated for sundry initial scenarios.
We estimate the shear and the bulk viscous coefficients for a hot hadronic gas mixture constituting of pions and nucleons. The viscosities are evaluated in the relativistic kinetic theory approach by solving the transport equation in the relaxation time approximation for binary collisions ($pipi$,$pi N$ and $NN$). Instead of vacuum cross-sections usually used in the literature we employ in-medium scattering amplitudes in the estimation of the relaxation times. The modified cross-sections for $pipi$ and $pi N$ scattering are obtained using one-loop modified thermal propagators for $rho$, $sigma$ and $Delta$ in the scattering amplitudes which are calculated using effective interactions. The resulting suppression of the cross sections at finite temperature and baryon density is observed to significantly affect the $T$ and $mu_N$ dependence of the viscosities of the system.
A simple geometrical model with event-by-event fluctuations is suggested to study elliptical and triangular eccentricities in the initial state of relativistic heavy-ion collisions. This model describes rather well the ALICE and ATLAS data for Pb+Pb collisions at center-of-mass energy $sqrt{s_{NN}} = 5.02$~TeV per nucleon pair, assuming that the second, $v_2$, and third, $v_3$, harmonics of the anisotropic flow are simply linearly proportional to the eccentricities $varepsilon_2$ and $varepsilon_3$, respectively. We show that the eccentricity $varepsilon_3$ has a pure fluctuation origin and is substantially dependent on the size of the overlap area only, while the eccentricity $varepsilon_2$ is mainly related to the average collision geometry. Elliptic flow, therefore, is weakly dependent on the event-by-event fluctuations everywhere except of the very central collisions 0--2%, whereas triangular flow is mostly determined by the fluctuations. The scaling dependence of the magnitude of the flow harmonics on atomic number, $v_n propto A^{-1/3}$, is predicted for this centrality interval.
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