  We analyze the quantum-classical crossover in the vicinity of the continuous
quantum critical point (QCP) of a Boson system. The analysis is based on the
Keldysh approach for the description of of the non-equilibrium quantum
dynamics. The critical behavior close to QCP has three different regimes
(modes): adiabatic quantum mode (AQM), dissipative classical mode (classical
critical dynamics mode (CCDM) and dissipative quantum critical mode (QCDM).
Crossover among these regimes (modes) is possible: it is shown that the
experimentally observed changing of the critical exponents close to QCP is the
dynamical effect accompanying the crossover from CCDM where the thermal
fluctuations dominate to QCDM where the quantum fluctuations determine the
critical behavior. In this case the effective dimension of the $d$-dimensional
system continuously changes from $D_{eff}=d$ to $D_{eff}=d+2$ while the
universality class of the system does not change.
