Abstract
For the Bjorken flow we investigate the hydrodynamization of different modes of the one-particle distribution function by analyzing its relativistic kinetic equations. We calculate the constitutive relations of each mode written as a multi-parameter trans-series encoding the non-perturbative dissipative contributions quantified by the Knudsen Kn and inverse Reynolds Re−1 numbers. At any given order in the asymptotic expansion of each mode, the transport coefficients get effectively renormalized by summing over all non-perturbative sectors appearing in the trans-series. This gives an effective description of the transport coefficients that provides a new renormalization scheme with an associated renormalization group equation, going beyond the realms of linear response theory. As a result, the renormalized transport coefficients feature a transition to their equilibrium fixed point, which is a neat diagnostics of transient non-Newtonian behavior. As a proof of principle, we verify the predictions of the effective theory with the numerical solutions of their corresponding evolution equations. Our studies strongly suggest that the phenomenological success of fluid dynamics far from local thermal equilibrium is due to the transient rheological behavior of the fluid.
Highlights
The regime of validity and applicability of relativistic hydrodynamics is linked with the proximity of the system to a local thermal equilibrium
The deformation history of the fluid is traced in the transport coefficients by considering their nonlinear functional dependence on the velocity gradient tensor, e.g. η ≡ η(σ μν ), which is often studied at a perturbative level in non-Newtonian fluid dynamics
We outlined a new method of decomposing the distribution function in terms of non-hydrodynamic modes in a suitable basis, which cast the Boltzmann equation into a dynamical system for a non-equilibrium scale-invariant expanding plasma
Summary
The regime of validity and applicability of relativistic hydrodynamics is linked with the proximity of the system to a local thermal equilibrium. A. Behtash et al / Physics Letters B 797 (2019) 134914 non-perturbative contributions as possible, to the transient nonhydrodynamic modes, which naturally build up the formal exponential solutions to the fluid evolution equations. Behtash et al / Physics Letters B 797 (2019) 134914 non-perturbative contributions as possible, to the transient nonhydrodynamic modes, which naturally build up the formal exponential solutions to the fluid evolution equations This provides renormalization group (RG) equations governing the RG flows of the dynamical transport coefficients, which by construction, converge to the correct values as the fluid reaches the thermal equilibrium. Being able to go beyond the attracting region distinguishes the predictions of linear response theory and the physics of non-equilibrated fluid dynamics
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