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SUMMARY:Non-linear dynamical systems approach to out of equilibrium hydrod
ynamical attractors: the Gubser flow case
DTSTART;VALUE=DATE-TIME:20180515T173500Z
DTEND;VALUE=DATE-TIME:20180515T174000Z
DTSTAMP;VALUE=DATE-TIME:20200711T040749Z
UID:indico-contribution-2871137@indico.cern.ch
DESCRIPTION:Speakers: NikolĂˇs Cruz Camacho (Universidad Nacional de Colom
bia)\nAttractors for relativistic hydrodynamics have been found recently i
n weakly and strong coupling physical systems. The existence of hydrodynam
ical attractor provides a firm theoretical foundation for the applicabilit
y of hydrodynamics in far-from-equilibrium conditions. In this work we exp
lain how the non-equilibrium attractors of systems undergoing Gubser flow
within relativistic kinetic theory can be established on general grounds b
y using methods of nonlinear dynamical systems. Namely we find the fixed p
oints and investigate the structure of flow diagrams of the evolution equa
tions and characterize the basin of attraction using a Lyapunov function n
ear the stable fixed point. We obtain the attractors of anisotropic hydrod
ynamics\, Israel-Stewart (IS) and transient fluid (DNMR) theories and show
that they are indeed non-planar and the basin of attraction is essentiall
y three dimensional. The attractors of each hydrodynamical model are compa
red with the one obtained from the exact Gubser solution of the Boltzmann
equation within the relaxation time approximation. We observe that the ani
sotropic hydrodynamics is able to match up to high numerical accuracy the
attractor of the exact solution while the second order hydrodynamical theo
ries fail to describe it. Our findings indicate that anisotropic hydrodyna
mics is an effective theory for far-from-equilibrium fluid dynamics which
resums the Knudsen and inverse Reynolds numbers to all orders.\n\nhttps://
indico.cern.ch/event/656452/contributions/2871137/
LOCATION:Palazzo del CasinĂ˛ First floor and third floor
URL:https://indico.cern.ch/event/656452/contributions/2871137/
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