  We study particle production and its density evolution and equilibration in
hot dense medium. One type of hot dense medium, which we study, is hadronic gas
produced at quark gluon plasma hadronization in heavy ions collisions in SPS,
RHIC and LHC experiments. We study hadron production at non-equilibrium quark
gluon plasma hadronization and their evolution in thermal hadronic gas phase.
We use non-equilibrium hadronization as the initial condition in the study of
hadronic kinetic phase. During this time period some hadronic resonances can be
produced in lighter hadrons fusion. Production of resonances is dominant over
decay if there is non-equilibrium excess of decay products. Within this model
we explain apparently contradictory experimental results reported in RHIC
experiments: Sigma(1385) yield is enhanced while Lambda(1520) yield is
suppressed compared to the statistical hadronization model expectation obtained
without kinetic phase. We also predict Delta(1232) enhancement. The second type
of plasma medium we consider is the relativistic electron positron photon
plasma drop. This plasma is expected to be produced in decay of supercritical
field created in ultrashort laser pulse. We study at what conditions this
plasma drop is opaque for photons and therefore may reach thermal and chemical
equilibrium. Further we consider muon and pion production in this plasma also
as a diagnostic tool. Finally all these theoretical developments can be applied
to begin a study of particles evolution in early universe in temperatures
domain from QGP hadronization (160 MeV) to nucleosynthesis (0.1 MeV). The first
results on pion equilibration are presented here.
