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<p>Theory Center Seminar<br>
Monday, Dec. 4, 2017<br>
1:00 p.m. (coffee at 12:45 p.m.)<br>
CEBAF Center, Room L102<br>
<br>
Mauricio Martinez Guerrero<br>
North Carolina State University<br>
<br>
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<font size="+1"><b>Far-from-Equilibrium Attractors and Nonlinear
Dynamical Systems </b></font><br>
<font size="+1"><b>Approach </b><b>to Relativistic Hydrodynamics</b></font><br>
<br>
The non-equilibrium attractors of systems undergoing Gubser flow
within relativistic kinetic theory<br>
are studied. In doing so we employ well-established methods of
nonlinear dynamical systems which<br>
rely on finding the fixed points, investigating the structure of
the flow diagrams of the evolution <br>
equations, and characterizing the basin of attraction using a
Lyapunov function near the stable<br>
fixed points. We obtain the attractors of anisotropic
hydrodynamics, Israel-Stewart (IS) and transient <br>
fluid (DNMR) theories and show that they are indeed non-planar and
the basin of attraction is essentially <br>
three dimensional. The attractors of each hydrodynamical model are
compared with the one obtained <br>
from the exact Gubser solution of the Boltzmann equation within
the relaxation time approximation. <br>
We observe that the anisotropic hydrodynamics is able to match up
to high numerical accuracy the attractor <br>
of the exact solution while the second order hydrodynamical
theories fail to describe it. We show that the<br>
IS and DNMR asymptotic series expansion diverge and use resurgence
techniques to perform the resummation <br>
of these divergences. We also comment on a possible link between
the manifold of steepest descent paths in <br>
path integrals and basin of attraction for the attractors via
Lyapunov functions that opens a new horizon toward<br>
effective field theory description of hydrodynamics. Our findings
indicate that anisotropic hydrodynamics is an <br>
effective theory for far-from-equilibrium fluid dynamics which
resums the Knudsen and inverse Reynolds<br>
numbers to all orders. </div>
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