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We study a relativistic fluid with longitudinal boost invariance in a quantum-statistical framework as an example of a solvable nonequilibrium problem. For the free quantum field, we calculate the exact form of the expectation values of the stress-energy tensor and the entropy current. For the stress-energy tensor, we find that a finite value can be obtained only by subtracting the vacuum of the density operator at some fixed proper time τ0. As a consequence, the stress-energy tensor acquires nontrivial quantum corrections to the classical free-streaming form.
In local scalar quantum field theories at finite temperature correlation functions are known to satisfy certain nonperturbative constraints, which for two-point functions in particular implies the existence of a generalization of the standard Källén-Lehmann representation. In this work, we use these constraints in order to derive a spectral representation for the shear viscosity arising from the thermal asymptotic states, η0. As an example, we calculate η0 in ϕ4 theory, establishing its leading behavior in the small and large coupling regimes.
We study how the mass and magnetic moment of the quarks are dynamically generated in nonequilibrium quark matter. We derive the equal-time transport and constraint equations for the quark Wigner function in a magnetized quark model and solve them in the semi-classical expansion. The quark mass and magnetic moment are self-consistently coupled to the Wigner function and controlled by the kinetic equations. While the quark mass is dynamically generated at the classical level, the quark magnetic moment is a pure quantum effect, induced by the quark spin interaction with the external magnetic field.
We present a new derivation of second-order relativistic dissipative fluid dynamics for quantum systems using Zubarev’s formalism for the non-equilibrium statistical operator. In particular, we discuss the shear-stress tensor to second order in gradients and argue that the relaxation terms for the dissipative quantities arise from memory effects contained in the statistical operator. We also identify new transport coefficients which describe the relaxation of dissipative processes to second order and express them in terms of equilibrium correlation functions, thus establishing Kubo-type formulae for the second-order transport coefficients.
In the initial stage of relativistic heavy-ion collisions, strong magnetic fields appear due to the large velocity of the colliding charges. The evolution of these fields appears as a novel and intriguing feature in the fluid-dynamical description of heavy-ion collisions. In this work, we study analytically the one-dimensional, longitudinally boost-invariant motion of an ideal fluid in the presence of a transverse magnetic field. Interestingly, we find that, in the limit of ideal magnetohydrodynamics, i.e., for infinite conductivity, and irrespective of the strength of the initial magnetization, the decay of the fluid energy density e with proper time τ is the same as for the time-honoured “Bjorken flow” without magnetic field. Furthermore, when the magnetic field is assumed to decay , where a is an arbitrary number, two classes of analytic solutions can be found depending on whether a is larger or smaller than one. In summary, the analytic solutions presented here highlight that the Bjorken flow is far more general than formerly thought. These solutions can serve both to gain insight on the dynamics of heavy-ion collisions in the presence of strong magnetic fields and as testbeds for numerical codes.
We derive the equations of second order dissipative fluid dynamics from the relativistic Boltzmann equation following the method of W. Israel and J. M. Stewart [1]. We present a frame independent calculation of all first- and second-order terms and their coefficients using a linearised collision integral. Therefore, we restore all terms that were previously neglected in the original papers of W. Israel and J. M. Stewart.
To investigate the formation and the propagation of relativistic shock waves in viscous gluon matter we solve the relativistic Riemann problem using a microscopic parton cascade. We demonstrate the transition from ideal to viscous shock waves by varying the shear viscosity to entropy density ratio n/s. Furthermore we compare our results with those obtained by solving the relativistic causal dissipative fluid equations of Israel and Stewart (IS), in order to show the validity of the IS hydrodynamics. Employing the parton cascade we also investigate the formation of Mach shocks induced by a high-energy gluon traversing viscous gluon matter. For n/s = 0.08 a Mach cone structure is observed, whereas the signal smears out for n/s >=0.32.
We calculate low-energymeson decay processes and pion-pion scattering lengths in a two-flavour linear sigma model with global chiral symmetry, exploring the scenario in which the scalar mesons f0(600) and a0(980) are assumed to be ¯qq states.
We discuss the phase diagram of moderately dense, locally neutral three-flavor quark matter using the framework of an effective model of quantum chromodynamics with a local interaction. The phase diagrams in the plane of temperature and quark chemical potential as well as in the plane of temperature and lepton-number chemical potential are discussed.
We study the effect of neutrino trapping on the phase diagram of dense, locally neutral three-flavor quark matter within the framework of a Nambu--Jona-Lasinio model. In the analysis, dynamically generated quark masses are taken into account self-consistently. The phase diagrams in the plane of temperature and quark chemical potential, as well as in the plane of temperature and lepton-number chemical potential are presented. We show that neutrino trapping favors two-flavor color superconductivity and disfavors the color-flavor-locked phase at intermediate densities of matter. At the same time, the location of the critical line separating the two-flavor color-superconducting phase and the normal phase of quark matter is little affected by the presence of neutrinos. The implications of these results for the evolution of protoneutron stars are briefly discussed. PACS numbers: 12.39.-x 12.38.Aw 26.60.+c