[Jlab-seminars] Theory Center Seminar

[Mary Fox]

Theory Center Seminar
Monday, Dec. 4, 2017
1:00 p.m. (coffee at 12:45 p.m.)
CEBAF Center, Room L102

Mauricio Martinez Guerrero
North Carolina State University

*Far-from-Equilibrium Attractors and Nonlinear Dynamical Systems *
*Approach **to Relativistic Hydrodynamics*

The non-equilibrium 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 non-planar 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 expansion 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 basin of attraction for the attractors via Lyapunov 
functions that opens a new horizon toward
effective field theory description of hydrodynamics. Our findings 
indicate that anisotropic hydrodynamics is an
effective theory for far-from-equilibrium fluid dynamics which resums 
the Knudsen and inverse Reynolds
numbers to all orders.
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