Hydrodynamics, resurgence, and transasymptotics

Başar, Gökçe; Dunne, Gerald V.

doi:10.1103/physrevd.92.125011

Cited by 93 publications

(120 citation statements)

References 43 publications

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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%

“…We take the late-time or asymptotic limit tanh 2 ρ ∼ 1 which was explained before and it poses no problem in the universality of the attractor due to the exponentially fast convergence of flow lines toward it at late times. In the case of IS and DNMR this constraint gives two different solutions so one chooses only the stable one A þ ðwÞ [25,26], which are respectively given by…”

Section: Universal Asymptotic Attractors For Different Dynamical mentioning

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%

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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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Section: Setupmentioning

confidence: 99%

Section: Universal Asymptotic Attractors For Different Dynamical mentioning

confidence: 99%

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

2018

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“…This suggests that hydrodynamic theory cannot be systematically improved by taking into account higher order-terms in the gradient series [26]. The gradient expansion generates an asymptotic series which exhibits initial signs of convergence for a few terms before eventually diverging [26,28]. The initial appearance of convergence may explain the observed remarkable phenomenological success of hydrodynamic formulations based on truncations of the gradient expansion at second or third order but, due to the ultimate divergence of the series, the theory cannot be improved beyond a certain order by keeping additional terms.…”

Section: Introductionmentioning

confidence: 99%

Exact solutions and attractors of higher-order viscous fluid dynamics for Bjorken flow

et al. 2019

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We consider causal higher order theories of relativistic viscous hydrodynamics in the limit of onedimensional boost-invariant expansion and study the associated dynamical attractor. We obtain evolution equations for the inverse Reynolds number as a function of Knudsen number. The solutions of these equations exhibit attractor behavior which we analyze in terms of Lyapunov exponents using several different techniques. We compare the attractors of the second-order Müller-Israel-Stewart (MIS), transient Denicol-Niemi-Molnar-Rischke (DNMR), and third-order theories with the exact solution of the Boltzmann equation in the relaxation-time approximation. It is shown that for Bjorken flow the third-order theory provides a better approximation to the exact kinetic theory attractor than both MIS and DNMR theories. For three different choices of the time dependence of the shear relaxation rate we find analytical solutions for the energy density and shear stress and use these to study the attractors analytically. By studying these analytical solutions at both small and large Knudsen numbers we characterize and uniquely determine the attractors and Lyapunov exponents. While for small Knudsen numbers the approach to the attractor is exponential, strong power-law decay of deviations from the attractor and rapid loss of initial state memory is found even for large Knudsen numbers. Implications for the applicability of hydrodynamics in far-offequilibrium situations are discussed.

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“…The strong coupling side of planar = 4 SU(N ) SYM can also be studied within the context of the AdS/CFT correspondence. In particular it was realised in [28] that the hydrodynamic gradient series for the strongly coupled = 4 super Yang-Mills plasma is only an asymptotic expansion leading to the works [29][30][31] dealing with resurgence and resummation issues in the fluid context of AdS 5 /CFT 4 .…”

Section: Introductionmentioning

confidence: 99%

The grin of Cheshire cat resurgence from supersymmetric localization

Dorigoni

Glass

2018

SciPost Phys.

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First we compute the S 2 partition function of the supersymmetric N −1 model via localization and as a check we show that the chiral ring structure can be correctly reproduced. For the 1 case we provide a concrete realisation of this ring in terms of Bessel functions. We consider a weak coupling expansion in each topological sector and write it as a finite number of perturbative corrections plus an infinite series of instantonanti-instanton contributions. To be able to apply resurgent analysis we then consider a non-supersymmetric deformation of the localized model by introducing a small unbalance between the number of bosons and fermions. The perturbative expansion of the deformed model becomes asymptotic and we analyse it within the framework of resurgence theory. Although the perturbative series truncates when we send the deformation parameter to zero we can still reconstruct non-perturbative physics out of the perturbative data in a nice example of Cheshire cat resurgence in quantum field theory. We also show that the same type of resurgence takes place when we consider an analytic continuation in the number of chiral fields from N to r ∈ . Although for generic real r supersymmetry is still formally preserved, we find that the perturbative expansion of the supersymmetric partition function becomes asymptotic so that we can use resurgent analysis and only at the end take the limit of integer r to recover the undeformed model.

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Hydrodynamics, resurgence, and transasymptotics

Cited by 93 publications

References 43 publications

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

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

Exact solutions and attractors of higher-order viscous fluid dynamics for Bjorken flow

The grin of Cheshire cat resurgence from supersymmetric localization

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