Resurgence for the non-conformal Bjorken flow with Fermi-Dirac and Bose-Einstein statistics

Abstract

We consider resurgence for the nonconformal Bjorken flow with Fermi-Dirac and Bose-Einstein statistics on the extended relaxation-time approximation. We firstly consider full formal transseries expanded around the equilibrium and then construct the resurgent relation by looking to the structure of Borel transformed ODEs. We form a conjecture of the resurgent relation based on the considerations that Stokes constants constituting of the resurgent relation originate only from singularities of dissipative variables on the Borel plane and that the other variables such as temperature and chemical potential become Borel nonsummable through nonlinear terms with the dissipative variables. We numerically check the conjecture for fundamental variables by explicitly evaluating values of the dominant Stokes constant depending on initial conditions and a particle mass. We also make comments on some issues related to transseries structure and resurgence such as the case of broken $U(1)$ symmetry, the massless case, generalized relaxation-time, and attractor solution.

v2: 49 pages, 4 figures, 2 tables, minor corrections

References in corpus (18)

• Dissipative relativistic fluid dynamics: a new way to derive the equations of motion from kinetic theory
• Transport Coefficients of Bulk Viscous Pressure in the 14-moment approximation
• Bulk viscosity-driven suppression of shear viscosity effects on the flow harmonics at RHIC
• Transport coefficients for bulk viscous evolution in the relaxation time approximation
• A kinetic regime of hydrodynamic fluctuations and long time tails for a Bjorken expansion
• On the hydrodynamic attractor of Yang-Mills plasma
• Novel Relaxation Time Approximation to the Relativistic Boltzmann Equation
• Hydrodynamic attractors in heavy ion collisions: a review
• Relativistic quantum transport coefficients for second-order viscous hydrodynamics
• Dynamical systems and nonlinear transient rheology of the far-from-equilibrium Bjorken flow
• Extended relaxation time approximation and relativistic dissipative hydrodynamics
• Causal first-order hydrodynamics from kinetic theory and holography
• Transasymptotics and hydrodynamization of the Fokker-Planck equation for gluons
• Exact-WKB analysis for SUSY and quantum deformed potentials: Quantum mechanics with Grassmann fields and Wess-Zumino terms
• Transport coefficients of second-order relativistic fluid dynamics in the relaxation-time approximation
• Hydrodynamic Attractor in a Hubble Expansion
• Far-from-equilibrium attractors for massive kinetic theory in the relaxation time approximation
• Novel features of attractors and transseries in non-conformal Bjorken flows