  If phase coherence determines the superconducting transition temperature Tc
in the cuprate oxides, it is of great interest to understand the role that
dynamics of the phase fluctuation plays in bringing about depletion of the
superconducting condensate. We will show that a phase correlation function can
be calculated that allows us to describe depletion of superconducting
condensate as a result of the quantum fluctuation. In two dimension, dynamic
phase fluctuation or pair fluctuation gives rise to a condensate depletion
linear with temperature as T$\to O$ in superconductors with nodes at the fermi
surface.
