  The non-equilibrium dynamics of the critical behaviour of the Boson system
undergoing the second order quantum phase transition is discussed. The analysis
is carried out using the Keldysh technique of the non-equilibrium dynamics
description. The critical behaviour close to the quantum critical point has
been shown to be multi-critical. Crossover among three different critical
regimes (modes) is possible: adiabatic quantum mode (AQM), dissipative
classical mode (classical critical dynamics mode (CCDM) and dissipative quantum
critical mode (QCDM). As a result, the observed critical behavior can
essentially depend on the conditions of approaching the critical point.
