Hydrodynamic attractors

RESUMO

Attractors are effective low-dimensional structures, defined in a chosen set of observables, that trajectories from different initial states approach; hydrodynamic attractors are those on which the late-time evolution is governed by hydrodynamic constitutive relations. Motivated by nuclear collisions and ultracold atomic gases, this chapter distinguishes attractorization (the loss of sensitivity to some directions in the space of initial states) from hydrodynamization (the onset of validity of hydrodynamic constitutive relations). Using mainly conformal, boost-invariant Bjorken flow, we compare Müller-Israel-Stewart-type theories, kinetic theory, holography, and classical Yang-Mills fields. Forward attraction, produced by the decay of non-hydrodynamic modes, is distinguished from pullback attraction, which can select a unique regular solution, and from expansion-driven attraction, which can suppress initial-state sensitivity before microscopic relaxation, with or without a subsequent fluid regime. Divergent gradient expansions and their transseries completions, the state-space picture, and adiabatic hydrodynamization provide complementary descriptions. Applications to nuclear collisions include particle production, transverse energy and flow, the initialization of and linear response around attracting backgrounds, jet quenching, and attractor-informed modifications of hydrodynamic models. For ultracold Fermi gases, we review theoretical proposals for bulk-channel attractors under scattering-length drives and distinguish them from recent measurements of short-time contact and momentum-distribution dynamics.