Ordering Dynamics of a Deeply Quenched Complex Field

A Statistical theory is presented for the ordering dynamics of a system with a complex order parameter quenched below the critical temperature. On the basis of a picture that string-like defects are formed in the early stage of the ordering process, the disappearing process of the defects is studied. We obtain the time evolution of the defect density and its two-point correlation function, which exhibits a scaling behavior, if the strings are initially convoluted and percolated. We also calculate the correlation function of the gradient of phase of the order parameter corresponding to the superfluid velocity in 4He. The characteristic length in this system is found to behave as t1/2.