Quantum critical dynamics of the boson system in the Ginzburg-Landau model

The quantum critical dynamics of the quantum phase transitions is considered. In the framework of the unified theory, based on the Keldysh technique, we consider the crossover from the classical to the quantum description of the boson many-body system dynamics close to the second order quantum phase transition. It is shown that in this case the upper critical space dimension of this model is dc+=2, therefore the quantum critical dynamics approach is useful in case of d<2. In the one-dimension system the phase coherence time does diverge at the quantum critical point, gc, and has the form of τ∝−ln∣g−gc∣/∣g−gc∣, the correlation radius diverges as rc∝∣g−gc∣−ν(ν=0.6).