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

We consider resurgence for the nonconformal Bjorken flow with Fermi-Dirac and Bose-Einstein statistics in the extended relaxation-time approximation. First, we examine the full formal transseries expanded around the equilibrium and then construct the resurgent relation by looking at the structure of Borel-transformed ordinary differential equations. We form a conjecture of the resurgent relation based on the consideration that the Stokes constants constituting 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 the values of the dominant Stokes constant depending on the initial conditions and the particle mass. We also comment 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 solutions. Published by the American Physical Society 2024