Far from equilibrium attractors in phase space

Abstract

The emergence of far from equilibrium, prehydrodynamic attractors is an important feature of boost-invariant flow in models of relativistic fluid dynamics, as well as in some microscopic theories. Originally, these attractors were defined in terms of attractor solutions, using a partial decoupling of the equations of motion that relied on using special variables. Reliance on such a decoupling restricts the class of systems that can be analysed. Instead of introducing special variables, here we directly leverage the singularity of the evolution equations at early proper time. This singularity is a consequence of boost invariance, which should be regarded as crucial physical input stemming from fundamental properties of particle production in QCD. We posit that it provides initial conditions which determine the attractor hypersurface in phase space, irrespective of whether the evolution equations can be partially decoupled or not. We validate this in a case where the equations of motion cannot be decoupled but the attractor can still be identified and governs the behaviour of generic solutions in a similar way to what happens in cases where attractor solutions exist.