Abstract
Hydrodynamic attractors have recently gained prominence in the context of early stages of ultrarelativistic heavy-ion collisions at the RHIC and LHC. We critically examine the existing ideas on this subject from a phase space point of view. In this picture the hydrodynamic attractor can be seen as a special case of the more general phenomenon of dynamical dimensionality reduction of phase space regions. We quantify this using principal component analysis. Furthermore, we adapt the well known slow-roll approximation to this setting. These techniques generalize easily to higher dimensional phase spaces, which we illustrate by a preliminary analysis of a dataset describing the evolution of a five-dimensional manifold of initial conditions immersed in a 16-dimensional representation of the phase space of the Boltzmann kinetic equation in the relaxation time approximation.
Highlights
Models of hydrodynamics.—We primarily focus on hydrodynamic theories, which despite their name include transient nonhydrodynamic excitations needed to avoid acausality
The hydrodynamic attractor was originally observed in this model in Ref. [2] using a special scale-invariant parametrization involving pressure anisotropy
The process of information loss occurs in three phases: local dimensionality reduction, approach to the hydrodynamic attractor loci, and evolution toward equilibrium along the attractor
Summary
In this picture the hydrodynamic attractor can be seen as a special case of the more general phenomenon of dynamical dimensionality reduction of phase space regions. The hydrodynamic attractor was originally observed in this model in Ref. The second hydrodynamic theory of interest here is the Heller-Janik-Spalinski-Witaszczyk (HJSW) model [55]
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