Novel Relaxation Time Approximation to the Relativistic Boltzmann Equation

Rocha, Gabriel S.; Denicol, Gabriel S.; Noronha, Jorge

doi:10.1103/physrevlett.127.042301

Cited by 74 publications

(44 citation statements)

References 50 publications

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“…to describe a conformal system with constant shearviscosity to entropy density ratio η/s. Energymomentum conservation requires that the local equilibrium temperature T and rest-frame velocity u µ are determined via the Landau matching condition [60][61][62][63][64] u ν T µν = u µ (7) with timelike four-velocity eigenvector u µ u µ = +1 and eigenvalue , representing the energy in the local restframe. The temperature T can be computed from the energy density via the equation of state…”

Section: Effective Kinetic Description Of Anisotropic Flowmentioning

confidence: 99%

Development of transverse flow at small and large opacities in conformal kinetic theory

Ambrus,

Schlichting,

Werthmann

2021

Preprint

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Section: Effective Kinetic Description Of Anisotropic Flowmentioning

confidence: 99%

Development of transverse flow at small and large opacities in conformal kinetic theory

Ambrus,

Schlichting,

Werthmann

2021

Preprint

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“…This approximation does not guarantee that the conservation laws related to particle number, energy and momentum are satisfied. Instead, we follow the novel relaxation time approximation presented in [27], which is free from such flaws. This approximation reads,…”

Section: Collision Term Approximationmentioning

confidence: 99%

“…n denotes the n-th associated Laguerre polynomial. In this formulation of the relaxation time approximation, an energy-dependent τ R can be used with any matching condition [27] -something that is not possible when employing the Anderson-Witting approximation for the collision term.…”

Section: Collision Term Approximationmentioning

confidence: 99%

“…Equations ( 56),( 59), ( 61) and (62) reduce to the traditional Israel-Stewart equations [9] if one fixes Landau matching conditions (q, s, z) = (1, 2, 1) [30]. But since we are using a more general relaxation time approximation [27], we can now calculate the transport coefficients of Israel-Stewart theory considering relaxation times that depend on energy. In Fig.…”

Section: Non-equilibrium Corrections To Particle and Energy Densitiesmentioning

confidence: 99%

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Transient fluid dynamics with general matching conditions: a first study from the method of moments

Rocha,

Denicol

2021

Preprint

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Recent works have revealed that matching conditions play a major role on general consistency properties of relativistic fluid dynamics such as causality, stability and wellposedness of the equations of motion. In this paper we derive transient fluid dynamics from kinetic theory, using the method of moments as proposed by Israel and Stewart, without imposing an specific matching condition. We then investigate how the equations of motion and their corresponding transport coefficients are affected by the choice of matching condition. I. INTRODUCTIONRelativistic fluid dynamics is an effective theory derived to describe the long-distance, long-time dynamics of a given microscopic theory. It is applied in several fields of physics, from the description of neutron star mergers [1,2] to the hot and dense nuclear matter produced in ultra-relativistic heavy ion collisions [3][4][5]. Nevertheless, the theoretical foundations of relativistic dissipative fluid dynamics remain open, still being topic of intense investigation [6,7].Relativistic generalizations of Navier-Stokes theory display physical and mathematical pathologies which practically prevents its use in general applications. The main issue is that Navier-Stokes theory is acausal and displays intrinsic instabilities [8] when perturbed around a global equilibrium state -an illness that cannot be corrected by adjusting matching conditions or transport coefficients. An early attempt to derive a linearly causal and stable fluid-dynamical theory was put forward by Israel and Stewart in the 1970's [9, 10]. The main feature of Israel-Stewart theory is that, instead of imposing constitutive relations relating the dissipative currents with derivatives of the velocity field, they promoted the non-equilibrium fields to independent dynamical variables for which they derived relaxation equations. Then, the requirements of linear causality and stability yield constrains on the relaxation times that are allowed in the formulation [11][12][13][14]. Even so, in Israel-Stewart theories, existence and uniqueness of solutions are not guaranteed in general curved spaces [15].Recently, Bemfica, Disconzi and Noronha proposed a novel theory of fluid dynamics which is not derived following the procedure outlined by . Other aspects about this formulation were also investigated in Refs. [18,19]. In this approach, fluid dynamics is constructed from a generalized gradient expansion, which includes both time-like and space-like gradients. This is in contrast to the traditional approach, used to derive Navier-Stokes theory, which consists of an expansion only in space-like gradients. It was then demonstrated that a first order theory in such generalized gradient expansion can lead to a causal and linearly stable theory as long as appropriate matching conditions are imposed.Matching conditions are constraints required to define the local equilibrium state of a fluid in the presence of dissipation, i.e., they define the temperature, chemical potential, and velocity of a viscous fluid. These conditi...

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“…Recent studies suggest, that momentum dependence of relaxation time can be related to the microscopic interaction relevant for the medium under consideration [20]. These two facts provide a strong motivation to use momentum dependent relaxation time approximation (MDRTA) in the relativistic transport equation to define the inhomogeneous part of the solution [21][22][23][24][25][26]. In the present work, we employ MDRTA to analytically calculate the exact values of the coefficients in the constitutive relations of hydrodynamic field redefinition from the kinetic theory in a general frame, i.e., for arbitrary matching conditions.…”

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confidence: 99%

Is first-order relativistic hydrodynamics in general frame stable and causal for arbitrary interaction?

Biswas,

Mitra,

Roy

2022

Preprint

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We derive a first-order, stable and causal, relativistic hydrodynamic theory from the microscopic kinetic equation using the gradient expansion technique in a general frame. The general frame is introduced from the arbitrary matching conditions for hydrodynamic fields. The interaction is introduced in the relativistic Boltzmann equation through momentum-dependent relaxation time approximation (MDRTA). We demonstrate here for the first time that not only the general frame choice but also the momentum dependence of microscopic interaction rate, captured through MDRTA, is imperative for producing the essential field corrections that give rise to a causal and stable first-order theory.

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Novel Relaxation Time Approximation to the Relativistic Boltzmann Equation

Cited by 74 publications

References 50 publications

Development of transverse flow at small and large opacities in conformal kinetic theory

Development of transverse flow at small and large opacities in conformal kinetic theory

Transient fluid dynamics with general matching conditions: a first study from the method of moments

Is first-order relativistic hydrodynamics in general frame stable and causal for arbitrary interaction?

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