\( \newcommand{\dd}{\mathrm{d}} \) \(
\DeclareMathOperator{\sign}{sign} \) \(
\newcommand{\pvec}[1]{\vec{#1}^{\,\prime}} \) \(
\newcommand{\R}{\mathbb{R}} \)

\( \newcommand{\dd}{\mathrm{d}} \) \(
\DeclareMathOperator{\sign}{sign} \)

# **Special Nuclear Theory Seminar**

Venue: Physics
Building, Max-von-Laue-Str. 1, Seminar Room PHYS 2.116

Time: Thursday, February 01, 4:30pm (s.t.)

Contact: hees@fias.uni-frankfurt.de

# Divergence of the gradient and slow-roll expansions and the validity of
hydrodynamics

## Gabriel Denicol (Universidade Federal
Fluminense, NiteroĢi, Brazil)

The applicability of hydrodynamics in describing the extreme conditions
produced in heavy ion collisions has still not been properly justified
from a theoretical point of view. Even more, the gradient expansion,
commonly used to derive hydrodynamics from microscopic theory, has been
recently shown to diverge for conformal fluids or relativistic gases
undergoing Bjorken flow, putting under question the definition of
hydrodynamics itself. Alternative derivations of the hydrodynamic series
have been proposed recently, such as the slow-roll expansion or a
generalized Chapman-Enskog expansion, and can be promising candidates to
define hydrodynamics.

In this talk, I discuss and present general analytical and
semi-analytical solutions of the hydrodynamic attractor of
Israel-Stewart theory and kinetic theory for Bjorken expanding fluids.
We show that the gradient expansion diverges and, for Israel-Stewart
theory, we show that even the slow-roll expansion, a commonly used
approach to characterize the attractor, diverges. We find that there are
examples in which the gradient expansion converges, but only for
parameters choices which violate causality.