Relating the Lyapunov exponents to transport coefficients in kinetic theory

Abstract

In this contribution, we report our recent findings on the phenomenological applications of non-equilibrium attractors to transport phenomena in fluid dynamics. Within the kinetic theory description, we study the non-linear hydrodynamization processes of a relativistic fluid undergoing Bjorken flow. The mathematical problem of solving the Boltzmann equation with a time-dependent relaxation time is recast into an infinite set of nonlinear ordinary differential equations for the moments of the one-particle distribution function. The constitutive relations of each non-hydrodynamic mode can be written as a multi-parameter trans-series that encodes the non-perturbative dissipative contributions quantified by the Knudsen Kn and inverse Reynolds Re−1 numbers. At a given order in the gradient expansion, we show that summing over all the non-perturbative sectors leads to a renormalized transport coefficient. The universal behavior of the renormalized shear viscosity is determined by the Lyapunov exponent and the anomalous dimension of the first moment at the stable fixed point. We comment on the relation between our findings and the physics of non-Newtonian fluids.