Understanding the early out-of-equilibrium dynamics of heavy-ion collisions (HIC) remains one
of the biggest theory challenges. So far, there are no first principle calculations for the equilibration
process of the quark gluon plasma and the dynamics close to the phase transition. In particular
describing the behavior close to the conjectured critical point, where critical slowing down leads
to off-equilibrium dynamics, poses difficulties.
Here we study the initial stages of a HIC using a low-energy effective theory of QCD, the
quark-meson model, in order to gain insight into the thermalization process. This model manifests
a central and physically relevant feature of QCD: chiral symmetry breaking in vacuum and its
restoration at finite temperature and density. At the critical endpoint this model is expected to
be in the same universality class as QCD and hence a viable model to explore dynamical critical
We solve the non-perturbative real-time quantum equations of motions for the quark and meson
fields in the two-particle irreducible effective action framework. Similar to a HIC, our system is
prepared in a high-energy initial state and suddenly quenched out of equilibrium, evolving towards
a thermal final state in the chirally broken phase.
In a first step, we investigate the time-evolution of both bulk and spectral properties of this
system, which provides us with insight into the approach of thermalization over time and the
properties of the relevant degrees of freedom dominating the real-time dynamics. For the thermal
final state, this implies information about the mass spectrum and the thermalization temperature.
Finally, the prospects of generalizing the simulations to finite baryon density and the approach to
the critical point are discussed.
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