[Theory-seminars] Today's seminar

[Bipasha Chakraborty]

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. 

-- 
Post-doctoral researcher 
Theory Center 
Jefferson Laboratory 
12000 Jefferson Avenue, Suite #1 
Newport News, VA 23606 
USA 

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