We use Lagrangian effective field theory techniques to construct the equations of motion for an ideal relativistic fluid whose constituent degrees freedom have microscopic polarization. discuss meaning such a system, and argue that it is first term in EFT appropriate describing polarization observables heavy ion collisions, as final state particle chiral magnetic vortaic effects. show this system will generally require non-dissipative dynamics at higher order gradient than second order,...

The earlier projection method introduced for boost-invariant and cylindrically symmetric systems is used to introduce a new formulation of anisotropic hydrodynamics that allows three substantially different values pressure acting locally in directions. Our considerations are based on the Boltzmann kinetic equation with collision term treated relaxation-time approximation momentum anisotropy included explicitly leading distribution function. A novel feature our work complete analysis second...

We discuss the concept of local thermodynamical equilibrium in relativistic hydrodynamics flat spacetime a quantum statistical framework without an underlying kinetic description, suitable for strongly interacting fluids. show that appropriate definition naturally leads to introduction hydrodynamical frame which four-velocity vector is one thermometer at with fluid, parallel inverse temperature four-vector $$\beta $$ , then becomes primary quantity. this most expansion stress-energy tensor...

We extend the effective theory approach to ideal fluid limit where polarization of is non-zero. After describing and motivating equations motion, we expand them around hydrostatic limit, obtaining sound wave vortex degrees freedom. discuss how presence affects stability causality limit.

Received 2 October 2017DOI:https://doi.org/10.1103/PhysRevD.96.079901© 2017 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasRelativistic heavy-ion collisionsTechniquesRelativistic hydrodynamicsFluid DynamicsParticles & Fields

Following the recent success of anisotropic hydrodynamics, I propose here a new, general prescription for hydrodynamic expansion around an background. The distribution fixes exactly complete energy-momentum tensor, just like effective temperature proper energy density in ordinary local equilibrium. This means that momentum anisotropies are already included at leading order, allowing large pressure without need next-to-leading-order treatment. first moment Boltzmann equation (local...

The framework of anisotropic hydrodynamics is generalized to include finite particle masses. Two schemes are introduced and their predictions compared with exact solutions the kinetic equation in relaxation time approximation. first formulation uses zeroth moments equation, whereas second moments. For case one-dimensional boost-invariant expansion, our numerical results indicate that yields much better agreement solutions.

We extend the derivation of second-order relativistic viscous hydrodynamics to incorporate effects baryon current, a nonvanishing chemical potential, and realistic equation state. Starting from microscopic quantum theory, we employ quasiparticle approximation describe evolution hydrodynamic degrees freedom establish its connection Wigner formalism. Using methods kinetic perform expansion derive closed set equations for components stress-energy tensor current. The resulting transport...

It is shown that different couples of stress-energy and spin tensors quantum-relativistic fields, which would be otherwise equivalent, are in fact inequivalent if the second law thermodynamics taken into account. The proof inequivalence based on analysis a macroscopic system at full thermodynamical equilibrium with total angular momentum specific instance given for free Dirac field, we show canonical Belinfante not equivalent. For this particular case, difference between predicted densities...

It is shown that different pairs of stress-energy and spin tensors quantum relativistic fields related by a pseudo-gauge transformation, i.e., differing divergence, imply mean values physical quantities in thermodynamical nonequilibrium situations. Most notably, transport coefficients the total entropy production rate are affected choice tensor field theory under consideration. Therefore, at least principle, it should be possible to disprove fundamental and/or show exists means dissipative...

We present the derivation of second-order relativistic viscous hydrodynamics from an effective Boltzmann equation for a system consisting quasiparticles single species. consider temperature-dependent masses and devise thermodynamically consistent framework to formulate evolution equations shear bulk pressure corrections. The main advantage this formulation is that one can consistently implement realistic state medium within kinetic theory. Specializing case one-dimensional purely...

A system of equations for anisotropic hydrodynamics is derived that describes a mixture quark and gluon fluids. The consistent treatment the zeroth, first, second moments kinetic allows us to construct new framework with more general forms phase-space distribution functions than used before. In this way, main deficiencies previous formulations mixtures are overcome good agreement exact kinetic-theory results obtained.

The one-dimensional non-boost-invariant evolution of the quark-gluon plasma, presumably produced during early stages heavy-ion collisions, is analyzed within frameworks viscous and anisotropic hydrodynamics. We neglect transverse dynamics assume homogeneous conditions in plane but, differently from Bjorken expansion, we relax longitudinal boost invariance order to study rapidity dependence various hydrodynamical observables. compare results obtained using several formulations second-order...

A novel description of kinetic theory dynamics is proposed in terms resummed moments that embed information both hydrodynamic and non-hydrodynamic modes. The resulting expansion can be used to extend hydrodynamics higher orders a consistent numerically efficient way; at lowest order it reduces an Israel-Stewart-like theory. This formalism especially suited investigate the general problem particles interacting with fields. We tested accuracy this approach against exact solution coupled...

In this work I develop a new framework for anisotropic hydrodynamics that generalizes the leading order of hydrodynamic expansion to full (3 + 1)-dimensional massive case. Following previous works, my considerations are based on Boltzmann kinetic equation with collisional term treated in relaxation time approximation. The momentum anisotropy is included explicitly term, allowing large difference between longitudinal and transverse pressures as well nontrivial dynamics. Energy conservation...

We study a relativistic fluid with longitudinal boost invariance in quantum-statistical framework as an example of solvable nonequilibrium problem. For the free quantum field, we calculate exact form expectation values stress-energy tensor and entropy current. tensor, find that finite value can be obtained only by subtracting vacuum density operator at some fixed proper time ${\ensuremath{\tau}}_{0}$. As consequence, acquires nontrivial corrections to classical free-streaming form.

The relativistic method of moments is one the most successful approaches to extract second order viscous hydrodynamics from a kinetic underlying background. equations can be systematically improved higher order, and they have already shown fast convergence results. In generalize that method, we introduced long range effects in form effective (medium dependent) masses gauge (coherent) fields. straightforward generalization hydrodynamic expansion problematic, or simply ill-defined, at order....

The collisionless Boltzmann equation, also called free-streaming, is a convenient approximation. It rather simple to implement numerically, and it effective at reducing the irregularities of rough initial conditions. can be obtained as small $\ensuremath{\hbar}$ limit from free scalar quantum field, namely, by neglecting ${\ensuremath{\hbar}}^{2}$ term in dynamical evolution Wigner distribution, precursor distribution function. In this work, general form for exact solutions presented, field...

Historically it has been believed that a time-independent classical source no effect on the scattering of relativistic uncharged field, in contrast with single particle quantum mechanics. In this work we show dynamics is not trivial. We solve exactly for amplitudes and find key ingredient production particles from unstable vacuum, conceptually similar to Schwinger mechanism. compute probabilities vacuum decay $n$ particles. The time dependence such displays interesting properties as Zeno...

Historically it has been believed that a time-independent classical source no effect on the scattering of relativistic uncharged fields, in contrast with single particle quantum mechanics. In this work we show dynamics is not trivial. We solve exactly for amplitudes and find key ingredient production particles from unstable vacuum, conceptually similar to Schwinger mechanism. compute probabilities vacuum decay <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"...

We extend the derivation of second-order relativistic viscous hydrodynamics to incorporate effects baryon current, a non-vanishing chemical potential, and realistic equation state. Starting from microscopic quantum theory, we employ quasiparticle approximation describe evolution hydrodynamic degrees freedom establish its connection Wigner formalism. Using methods kinetic perform expansion derive closed set equations for components stress-energy tensor current. The resulting transport...