Conformal Bjorken flow in the general frame and its attractor: Similarities and discrepancies with the Müller-Israel-Stewart formalism

Shokri, Masoud; Taghinavaz, F.

doi:10.1103/physrevd.102.036022

Cited by 21 publications

(9 citation statements)

References 41 publications

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“…Other important question is that to construct a holographic picture for the GF framework. Also there are some problems concerning the GF framework [14] which necessitate the use of higher order terms in the GF constitutive relations.…”

Section: Discussionmentioning

confidence: 99%

“…These observations have pushed theoretical works to study the late time behavior of QCD matter dynamics. There is a large literature in this field which states that an attractor solution appears in the hydrodynamics calculations regardless of any initial conditions, [9][10][11][12][13][14][15][16][17][18][19][20] and references therein. Having an attractor solution means that the RH can be applied to any high energetic collisions of particles -regardless of its size and at late times the "causal" RH equations can be used safely.…”

Section: Introductionmentioning

confidence: 99%

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Causality and stability conditions of a conformal charged fluid

Taghinavaz

2020

J. High Energ. Phys.

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In this paper, I study the conditions imposed on a normal charged fluid so that the causality and stability criteria hold for this fluid. I adopt the newly developed General Frame (GF) notion in the relativistic hydrodynamics framework which states that hydrodynamic frames have to be fixed after applying the stability and causality conditions. To do this, I take a charged conformal matter in the flat and 3 + 1 dimension to analyze better these conditions. The causality condition is applied by looking to the asymptotic velocity of sound hydro modes at the large wave number limit and stability conditions are imposed by looking to the imaginary parts of hydro modes as well as the Routh-Hurwitz criteria. By fixing some of the transports, the suitable spaces for other ones are derived. I observe that in a dense medium having a finite U(1) charge with chemical potential μ0, negative values for transports appear and the second law of thermodynamics has not ruled out the existence of such values. Sign of scalar transports are not limited by any constraints and just a combination of vector transports is limited by the second law of thermodynamic. Also numerically it is proved that the most favorable region for transports $$ {\tilde{\upgamma}}_{1,2}, $$ γ ˜ 1 , 2 , coefficients of the dissipative terms of the current, is of negative values.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Causality and stability conditions of a conformal charged fluid

Taghinavaz

2020

J. High Energ. Phys.

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“…One of the main concern regarding an infinite series expansions is the convergence features. The divergences which exist in the RH series in the real space [14] can be handled by using the Borel-Padé techniques [15][16][17][18][19]. This provides good information about the origin of divergent points and even the region in which the RH series might be convergent.…”

Section: Jhep05(2021)287mentioning

confidence: 99%

Critical behaviour of hydrodynamic series

Asadi

Soltanpanahi

Taghinavaz

2021

J. High Energ. Phys.

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We investigate the time-dependent perturbations of strongly coupled $$ \mathcal{N} $$ N = 4 SYM theory at finite temperature and finite chemical potential with a second order phase transition. This theory is modelled by a top-down Einstein-Maxwell-dilaton description which is a consistent truncation of the dimensional reduction of type IIB string theory on AdS5×S5. We focus on spin-1 and spin-2 sectors of perturbations and compute the linearized hydrodynamic transport coefficients up to the third order in gradient expansion. We also determine the radius of convergence of the hydrodynamic mode in spin-1 sector and the lowest non-hydrodynamic modes in spin-2 sector. Analytically, we find that all the hydrodynamic quantities have the same critical exponent near the critical point θ = $$ \frac{1}{2} $$ 1 2 . Moreover, we propose a relation between symmetry enhancement of the underlying theory and vanishing of the only third order hydrodynamic transport coefficient θ1, which appears in the shear dispersion relation of a conformal theory on a flat background.

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“…We believe that one of the the deepest insights on the issue of the diffusion equation being "right" or "wrong" has been given by Geroch [8]. He proposed that we should think of relation (76), not as an equation to be solved for arbitrary initial conditions, but rather as the observation that the difference between its two sides is too small to be measurable in many physical states. This point of view is fully confirmed by kinetic theory and by the work of Lindblom [72].…”

Section: Boost-generated Spurious Modesmentioning

confidence: 99%

“…It turns out that leaving T νρσi and N νσi completely free (without imposing any thermodynamical or geometrical constraint on them) allows one to regulate them in a way that both the gapped and the Hydro-modes decay with time. This enforces the stability of the theory [24,25,75] at the expenses of allowing for ∇ ν s ν < 0 when gradients are large [7,76]. This a posteriori regulation of T νρσi and N νσi is commonly referred to as choice of hydrodynamic frame (not to be confused with reference frame [24]), hence the name frame-stabilised theory.…”

Section: The Frame-stabilised First-order Approachmentioning

confidence: 99%

Unified Extended Irreversible Thermodynamics and the stability of relativistic theories for dissipation

Gavassino,

Antonelli

2021

Preprint

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In a relativistic context, the main purpose of Extended Irreversible Thermodynamics (EIT) is to generalize the principles of non-equilibrium thermodynamics to the domain of fluid dynamics. In particular, the theory aims at modelling any diffusion-type process (like heat as diffusion of energy, viscosity as diffusion of momentum, charge-conductivity as diffusion of particles) directly from thermodynamic laws. Although in Newtonian physics this task can be achieved with a firstorder approach to dissipation (i.e. Navier-Stokes-Fourier like equations), in a relativistic framework the relativity of simultaneity poses serious challenges to the first-order methodology, originating instabilities which are, instead, naturally eliminated within EIT. The first part of this work is dedicated to reviewing the most recent progress made in understanding the mathematical origin of this instability problem. In the second part, we present the formalism that arises by promoting non-equilibrium thermodynamics to a classical effective field theory. We call this approach Unified Extended Irreversible Thermodynamics (UEIT), because it contains, as particular cases, EIT itself, in particular the Israel-Stewart theory and the divergence-type theories, plus Carter's approach and most branches of non-equilibrium thermodynamics, such as relativistic chemistry and radiation hydrodynamics. We use this formalism to explain why all these theories are stable by construction (provided that the microscopic input is correct), showing that their (Lyapunov) stability is a direct consequence of the second law of thermodynamics.

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Conformal Bjorken flow in the general frame and its attractor: Similarities and discrepancies with the Müller-Israel-Stewart formalism

Cited by 21 publications

References 41 publications

Causality and stability conditions of a conformal charged fluid

Causality and stability conditions of a conformal charged fluid

Critical behaviour of hydrodynamic series

Unified Extended Irreversible Thermodynamics and the stability of relativistic theories for dissipation

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