Transseries for causal diffusive systems

Heller, Michał; Serantes, Alexandre; Spaliński, Michał; Svensson, Viktor; Withers, Benjamin

doi:10.1007/jhep04(2021)192

Cited by 9 publications

(5 citation statements)

References 75 publications

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“…This is different than the standard gradient expansion since in BDNK the constitutive relations contain time derivatives even in the local rest frame of the fluid. The large order behavior of the relativistic gradient series has been recently the focus of several works [106][107][108][109][110][111][112][113][114][115][116][117][118][119], and it would be interesting to extend such analyses to include the type of theories investigated here.…”

Section: Discussionmentioning

confidence: 99%

First-Order General-Relativistic Viscous Fluid Dynamics

Bemfica¹,

Disconzi²,

Noronha³

2020

Preprint

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We present the first example of a relativistic viscous fluid theory that satisfies all of the following properties: (a) the system coupled to Einstein's equations is causal and strongly hyperbolic; (b) equilibrium states are stable; (c) all leading dissipative contributions are present, i.e., shear viscosity, bulk viscosity, and thermal conductivity; (d) non-zero baryon number is included; (e) entropy production is non-negative in the regime of validity of the theory; (f) all of the above holds in the nonlinear regime without any simplifying symmetry assumptions; these properties are accomplished using a generalization of Eckart's theory containing only the hydrodynamic variables, so that no new extended degrees of freedom are needed as in Mueller-Israel-Stewart theories. Property (b), in particular, follows from a more general result that we also establish, namely, sufficient conditions that when added to stability in the fluid's rest frame imply stability in any reference frame obtained via a Lorentz transformation. All our results are mathematically rigorously established. The framework presented here provides the starting point for systematic investigations of general-relativistic viscous phenomena in neutron star mergers.

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Section: Discussionmentioning

confidence: 99%

First-Order General-Relativistic Viscous Fluid Dynamics

Bemfica¹,

Disconzi²,

Noronha³

2020

Preprint

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“…This provides good information about the origin of divergent points and even the region in which the RH series might be convergent. On the other hand, the convergence of the gradient expansion in real space can be related to the radius of convergence of RH in momentum space [20,21]. In the momentum space, the location of the singular points reflect the existence of non-hydro modes and the credit of the RH depends on the strength of hydro modes over non-hydro modes [22,23].…”

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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“…Along similar lines, resurgence has also been a fruitful tool for analysing hydrodynamics and its extensions, particularly in the context of holography (see refs. [10][11][12][13][14][15][16][17][18][19][20][21]). Among those and related studies, the best understood cases usually pertain to boost invariant (Bjorken-like) flows in 'position space' where one complexifies the proper time τ ∈ C. What most of the above quantum mechanical, quantum field theoretic, hydrodynamic and holographic studies share is the necessity for analysing asymptotic series, usually by the methods of Padé approximants, the Borel resummation and constructions of transseries that contain the knowledge of higher-energy modes.…”

Section: Introductionmentioning

confidence: 99%

Reconstruction of spectra and an algorithm based on the theorems of Darboux and Puiseux

Grozdanov

Lemut

2023

J. High Energ. Phys.

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Assuming only a known dispersion relation of a single mode in the spectrum of a meromorphic two-point function (in the complex frequency plane at fixed wavevector) in some quantum field theory, we investigate when and how the reconstruction of the complete spectrum of physical excitations is possible. In particular, we develop a constructive algorithm based on the theorems of Darboux and Puiseux that allows for such a reconstruction of all modes connected by level-crossings. For concreteness, we focus on theories in which the known mode is a gapless excitation described by the hydrodynamic gradient expansion, known at least to some (preferably high) order. We first apply the algorithm to a simple algebraic example and then to the transverse momentum excitations in the holographic theory that describes a stack of M2 branes and includes momentum diffusion as its gapless excitation.

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Transseries for causal diffusive systems

Cited by 9 publications

References 75 publications

First-Order General-Relativistic Viscous Fluid Dynamics

First-Order General-Relativistic Viscous Fluid Dynamics

Critical behaviour of hydrodynamic series

Reconstruction of spectra and an algorithm based on the theorems of Darboux and Puiseux

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