Hydrodynamization in kinetic theory: Transient modes and the gradient expansion

Heller, Michał; Kurkela, Aleksi; Spaliński, Michał; Svensson, Viktor

doi:10.1103/physrevd.97.091503

Cited by 161 publications

(184 citation statements)

References 67 publications

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“…The analysis of these large order perturbations showed that the hydrodynamic expansion is an asymptotic series, exhibiting a factorial growth of the series coefficients. Similar behaviour was found in different ultraviolet completions of second order hydrodynamics [26][27][28] and kinetic theory in the relaxation time approximation (RTA) [29] (see also [30] for a complementary analysis of the convergence of the hydrodynamic series). Interestingly, the analysis of these series via Borel-Padé techniques showed that these large order gradient expansions are sensitive to non-hydrodynamic modes, which play an equivalent role to non-perturbative corrections in perturbation theory.…”

Section: Jhep04(2018)042supporting

confidence: 68%

“…By varying the amplitude of those non-perturbative corrections we observe that the convergence of different initial configurations towards the attractor occurs at values of the viscosity-rescaled gradient for which the resummation has hydrodynamized. We also perform an identical analysis of the hydrodynamic series of RTA kinetic theory [29] and find that in this model both hydrodynamization and convergence to the attractor solution occurs at smaller viscosity-rescaled gradients than in the strong coupling computations. This paper is organised as follows: in section 2 we review the main properties of boost invariant flow and holographic Gauss-Bonnet to set up the notation, define the main quantities and outline the strategy to compute large order gradient corrections in this highercurvature theory.…”

Section: Jhep04(2018)042mentioning

confidence: 99%

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Resurgence and hydrodynamic attractors in Gauss-Bonnet holography

Casalderrey-Solana

Gushterov

Meiring

2018

J. High Energ. Phys.

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Abstract:We study the convergence of the hydrodynamic series in the gravity dual of Gauss-Bonnet gravity in five dimensions with negative cosmological constant via holography. By imposing boost invariance symmetry, we find a solution to the Gauss-Bonnet equation of motion in inverse powers of the proper time, from which we can extract high order corrections to Bjorken flow for different values of the Gauss-Bonnet parameter λ GB . As in all other known examples the gradient expansion is, at most, an asymptotic series which can be understood through applying the techniques of Borel-Padé summation. As expected from the behaviour of the quasi-normal modes in the theory, we observe that the singularities in the Borel plane of this series show qualitative features that interpolate between the infinitely strong coupling limit of N = 4 Super Yang Mills theory and the expectation from kinetic theory. We further perform the Borel resummation to constrain the behaviour of hydrodynamic attractors beyond leading order in the hydrodynamic expansion. We find that for all values of λ GB considered, the convergence of different initial conditions to the resummation and its hydrodynamization occur at large and comparable values of the pressure anisotropy.

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Section: Jhep04(2018)042supporting

confidence: 68%

Section: Jhep04(2018)042mentioning

confidence: 99%

Resurgence and hydrodynamic attractors in Gauss-Bonnet holography

Casalderrey-Solana

Gushterov

Meiring

2018

J. High Energ. Phys.

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“…In Minkowski space with 1 Previous studies of the Bjorken model have shown that after rewriting the hydrodynamical equations for the temperature and the only independent component of the shear viscous tensor in terms of the variable w ¼ τTðτÞ (where τ and T are the longitudinal proper time and temperature) reduce effectively to a truly 1D nonlinear differential equation [20,26,27,36,37]. The solution of this equation for a suitable initial condition determines what has been, by abuse of terminology, called the "attractor solution."…”

Section: Setupmentioning

confidence: 99%

“…Previous works have focused on fluids undergoing Bjorken flow [20,26,27,36,37] and nonhomogeneous expanding plasmas [39]. We expand these studies by investigating the properties of the attractors in the plasmas undergoing Gubser flow [40,41].…”

Section: Introductionmentioning

confidence: 99%

Far-from-equilibrium attractors and nonlinear dynamical systems approach to the Gubser flow

2018

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The nonequilibrium attractors of systems undergoing Gubser flow within relativistic kinetic theory are studied. In doing so we employ well-established methods of nonlinear dynamical systems which rely on finding the fixed points, investigating the structure of the flow diagrams of the evolution equations, and characterizing the basin of attraction using a Lyapunov function near the stable fixed points. We obtain the attractors of anisotropic hydrodynamics, Israel-Stewart (IS) and transient fluid (DNMR) theories and show that they are indeed nonplanar and the basin of attraction is essentially three dimensional. The attractors of each hydrodynamical model are compared with the one obtained from the exact Gubser solution of the Boltzmann equation within the relaxation time approximation. We observe that the anisotropic hydrodynamics is able to match up to high numerical accuracy the attractor of the exact solution while the second-order hydrodynamical theories fail to describe it. We show that the IS and DNMR asymptotic series expansions diverge and use resurgence techniques to perform the resummation of these divergences. We also comment on a possible link between the manifold of steepest descent paths in path integrals and the basin of attraction for the attractors via Lyapunov functions that opens a new horizon toward an effective field theory description of hydrodynamics. Our findings indicate that the reorganization of the expansion series carried out by anisotropic hydrodynamics resums the Knudsen and inverse Reynolds numbers to all orders and thus, it can be understood as an effective theory for the far-from-equilibrium fluid dynamics.

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“…It was concluded that a size of 0.5 fm was feasible, which was later refined to 1/T by an explicit computation using 5-dimensional numerical general relativity [35]. The second and third constraint are studied in [36][37][38][39], where it was concluded that hydrodynamics breaks down for momentum modes of |k| > 4.5T , which translates into a size λ 2π/|k| > 1.4/T . 2 So perhaps unsurprisingly all three constraints give a similar outcome.…”

Section: Small Systemsmentioning

confidence: 99%

Early hydrodynamisation, energy loss and small systems in holographic heavy ion collisions

Schee

2017

EPJ Web Conf.

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Abstract. There has been much recent progress in describing heavy ion collisions using strongly coupled methods. We start by introducing a few caveats in applying holography to QCD, after which we will highlight recent progress on the initial stage, by simulating shock collisions in the dual gravitational theory. Secondly, we describe an attempt at describing jet evolution through strongly coupled plasma, where we specifically also included the width of the jet, and the interplay of this width with the energy lost as the jet propagates through the plasma. Lastly, there has been much recent discussion about the formation of quark-gluon plasma in small systems at low multiplicies, such as produced in proton-nucleus or even proton-proton collisions. At infinitely strong coupling it is possible to estimate that this may be possible, provided that the particle multiplicity satisfies dN tot /dy 4. OutlineCare must always be taken when interpreting results from holography in relation to heavy ion collisions. Especially around the QCD confinement/deconfinement transition pure N = 4 SYM is different from QCD, although much progress can be made by considering more realistic holographic models including a running of the coupling constant and a confinement/deconfinement transition [1] . At high energy scales a direct comparison is also complicated, since asymptotic freedom implies that the coupling becomes weak at (very) high energies. The coupling, however, runs only logarithmically with energy, and hence at LHC energy scales there is always a need of including some strongly coupled physics.It is hence a sensible approach to model heavy ion collisions at weak coupling, using perturbative QCD, as well as to model the collisions at strong coupling, using holography. Combining insights from both approaches can then lead to a realistic understanding of heavy ion collisions. Here, we will give a recent overview of holographic attempts to describe the initial stage as well as the propagation of jets. Lastly, we comment on recent excitement where flow-like signals were observed in small systems at relatively low multiplicities. a

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Hydrodynamization in kinetic theory: Transient modes and the gradient expansion

Cited by 161 publications

References 67 publications

Resurgence and hydrodynamic attractors in Gauss-Bonnet holography

Resurgence and hydrodynamic attractors in Gauss-Bonnet holography

Far-from-equilibrium attractors and nonlinear dynamical systems approach to the Gubser flow

Early hydrodynamisation, energy loss and small systems in holographic heavy ion collisions

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