Dynamical systems approach to determine the far-from-equilibrium attractors for the Gubser flow

During the last decades it has been proven that relativistic hydrodynamics is a valuable phenomenological tool to describe high energy nuclear collisions. Recently, the research has focused on understanding the concept of hydrodynamical attractors within the different theories. Therefore, in this work 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 (aHydro), 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. Our findings indicate that the reorganization of the expansion series carried out by anisotropic hydrodynamics resums the Knudsen and inverse Reynolds numbers to all orders, thus it can be understood as an effective theory for the far-from-equilibrium fluid dynamics.

• Autores: Cruz Camacho, Carlos Nikolás; Martínez Guerrero, Mauricio; Pinilla Beltrán, Edna Carolina
• Fecha de publicación: 2019
• Institución: Universidad Nacional de Colombia
• Repositorio: Universidad Nacional de Colombia
• Idioma: spa
• OAI Identifier: oai:repositorio.unal.edu.co:unal/69319
• Acceso en línea: https://repositorio.unal.edu.co/handle/unal/69319; http://bdigital.unal.edu.co/70997/
• Palabra clave: 5 Ciencias naturales y matemáticas / Science; 53 Física / Physics; Relativistic Boltzmann equation; Kinetic theory; Hydrodynamization; Anisotropic hydrodynamics; Non-autonomous dynamical systems; Ecuación relativista de Boltzmann; Teoría cinética; Hidrodinización; Hidrodinámica anisotrópica; Sistemas dinámicos no; Autónomos
• Rights: openAccess
• License: Atribución-NoComercial 4.0 Internacional