@article{behtash_kamata_martinez_shi_2020, title={Global flow structure and exact formal transseries of the Gubser flow in kinetic theory}, ISSN={["1029-8479"]}, DOI={10.1007/JHEP07(2020)226}, abstractNote={Abstract
                     In this work we introduce the generic conditions for the existence of a non-equilibrium attractor that is an invariant manifold determined by the long-wavelength modes of the physical system. We investigate the topological properties of the global flow structure of the Gubser flow for the Israel-Stewart theory and a kinetic model for the Boltzmann equation by employing Morse-Smale theory. We present a complete classification of the invariant submanifolds of the flow and determine all the possible flow lines connecting any pair of UV/IR fixed points. The formal transseries solutions to the Gubser dynamical system around the early-time (UV) and late-time (IR) fixed points are constructed and analyzed. It is proven that these solutions are purely perturbative (or power-law asymptotic) series with a finite radius of convergence. Based on these analyses, we find that Gubser-like expanding kinetic systems do not hydrodynamize owing to the failure of the hydrodynamization process which heavily relies on the classification of (non)hydrodynamic modes in the IR regime. This is in contrast to longitudinal boost-invariant plasmas where the asymptotic dynamics is described by a few terms of the hydrodynamic gradient expansion. We finally compare our results for both Bjorken and Gubser conformal kinetic models.}, number={7}, journal={JOURNAL OF HIGH ENERGY PHYSICS}, author={Behtash, Alireza and Kamata, Syo and Martinez, Mauricio and Shi, Haosheng}, year={2020}, month={Jul} }
 @article{behtash_kamata_martinez_shi_2019, title={Dynamical systems and nonlinear transient rheology of the far-from-equilibrium Bjorken flow}, volume={99}, ISSN={["2470-0029"]}, DOI={10.1103/PhysRevD.99.116012}, abstractNote={In relativistic kinetic theory, the one-particle distribution function is approximated by an asymptotic perturbative power series in the Knudsen number which is divergent. For the Bjorken flow, we expand the distribution function in terms of its moments and study their nonlinear evolution equations. The resulting coupled dynamical system can be solved for each moment consistently using a multiparameter transseries which makes the constitutive relations inherit the same structure. A new nonperturbative dynamical renormalization scheme is born out of this formalism that goes beyond the linear response theory. We show that there is a Lyapunov function, also known as dynamical potential, which is, in general, a function of the moments and time satisfying Lyapunov stability conditions along renormalization group flows connected to the asymptotic hydrodynamic fixed point. As a result, the transport coefficients get dynamically renormalized at every order in the time-dependent perturbative expansion by receiving nonperturbative corrections present in the transseries. The connection between the integration constants and the UV data is discussed using the language of dynamical systems. Furthermore, we show that the first dissipative correction in the Knudsen number to the distribution function is not only determined by the known effective shear viscous term but also a new high-energy nonhydrodynamic mode. It is demonstrated that the survival of this new mode is intrinsically related to the nonlinear mode-to-mode coupling with the shear viscous term. Finally, we comment on some possible phenomenological applications of the proposed nonhydrodynamic transport theory.}, number={11}, journal={PHYSICAL REVIEW D}, author={Behtash, Alireza and Kamata, Syo and Martinez, Mauricio and Shi, Haosheng}, year={2019}, month={Jun} }