Derivation of nonlinear generalized equations of quantum relativistic hydrodynamics

Zubarev, D. N.; Prozorkevich, A. V.; Smolyanskii, S. A.

doi:10.1007/bf01032069

Cited by 109 publications

(137 citation statements)

References 12 publications

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“…The general covariant form of the local thermodynamic equilibrium density operator was introduced in [36][37][38] and lately discussed in detail in refs. [23,30,[39][40][41]:…”

Section: Global Thermodynamic Equilibrium Density Operatormentioning

confidence: 99%

General equilibrium second-order hydrodynamic coefficients for free quantum fields

Buzzegoli

Grossi

Becattini

2017

J. High Energ. Phys.

135

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We present a systematic calculation of the corrections of the stress-energy tensor and currents of the free boson and Dirac fields up to second order in thermal vorticity, which is relevant for relativistic hydrodynamics. These corrections are non-dissipative because they survive at general thermodynamic equilibrium with non vanishing mean values of the conserved generators of the Lorentz group, i.e. angular momenta and boosts. Their equilibrium nature makes it possible to express the relevant coefficients by means of correlators of the angular-momentum and boost operators with stress-energy tensor and current, thus making simpler to determine their so-called "Kubo formulae". We show that, at least for free fields, the corrections are of quantum origin and we study several limiting cases and compare our results with previous calculations. We find that the axial current of the free Dirac field receives corrections proportional to the vorticity independently of the anomalous term.

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“…The general covariant form of the local thermodynamic equilibrium density operator was introduced in [36][37][38] and lately discussed in detail in refs. [23,30,[39][40][41]:…”

Section: Global Thermodynamic Equilibrium Density Operatormentioning

confidence: 99%

General equilibrium second-order hydrodynamic coefficients for free quantum fields

Buzzegoli

Grossi

Becattini

2017

J. High Energ. Phys.

135

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“…This covariant form of a local equilibrium operator was, to our knowledge, first obtained with this variational method by Zubarev [21]. It is clear that the operator in (5) does depend on the particular hypersurface (τ ) (whence on the field n).…”

Section: Local Thermodynamical Equilibrium In Relativistic Quantum Stmentioning

confidence: 99%

Local thermodynamical equilibrium and the $$\beta $$ β frame for a quantum relativistic fluid

et al. 2015

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We discuss the concept of local thermodynamical equilibrium in relativistic hydrodynamics in flat spacetime in a quantum statistical framework without an underlying kinetic description, suitable for strongly interacting fluids. We show that the appropriate definition of local equilibrium naturally leads to the introduction of a relativistic hydrodynamical frame in which the four-velocity vector is the one of a relativistic thermometer at equilibrium with the fluid, parallel to the inverse temperature four-vector β, which then becomes a primary quantity. We show that this frame is the most appropriate for the expansion of the stress-energy tensor from local thermodynamical equilibrium and that therein the local laws of thermodynamics take on their simplest form. We discuss the difference between the β frame and Landau frame and present an instance where they differ.

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“…The nonequilibrium state of such a system is described by a relativistic quantum nonequilibrium statistical operator ̺(t) which satisfies the relativistic Liouville equation admitting an obviously covariant form. Such a Liouville equation for a thermal quantum field system in a covariant form in the interaction representation was written down in [ 67,70] on the basis of the Tomonaga-Schwinger equation [ 71,72] in the next form:…”

Section: Thermo Field Transport Equations For a Quark-gluon Plasmamentioning

confidence: 99%

Thermo Field Hydrodynamic and Kinetic Equations of Dense Quantum Nuclear Systems

Tokarchuk¹,

Arimitsu²,

Kobryn³

1998

Condens. Matter Phys.

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Basic equations of nonequilibrium thermo field dynamics of dense quantum systems are presented. A formulation of nonequilibrium thermo field dynamics has been performed using the nonequilibrium statistical operator method by D.N.Zubarev. Hydrodynamic equations have been obtained in thermo field representation. Two levels of the description of kinetics and hydrodynamics of a dense nuclear matter are considered. The first one is a quantum system with strongly coupled states, the second one is a quarkgluon plasma. Generalized transfer equations of a consistent description of kinetics and hydrodynamics have been obtained, as well as limiting cases are considered.

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Derivation of nonlinear generalized equations of quantum relativistic hydrodynamics

Cited by 109 publications

References 12 publications

General equilibrium second-order hydrodynamic coefficients for free quantum fields

General equilibrium second-order hydrodynamic coefficients for free quantum fields

Local thermodynamical equilibrium and the $$\beta $$ β frame for a quantum relativistic fluid

Thermo Field Hydrodynamic and Kinetic Equations of Dense Quantum Nuclear Systems

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