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We investigate, via numerical simulations, the phase ordering kinetics of atwo- dimensional soft-spin O(2) Ginzburg-Landau model when a reversible modecou- pling is included via the conserved conjugate momentum of the spin orderparameter (the model E). Coarsening of the system, when quenched from a dis-ordered state to zero temperature, is observed to be enhanced by the existenceof the mode coupling terms. The growth of the characteristic length scale L(t)exhibits an effective super-diffusive growth exponent that can be interpretedas a positive logarithmic-like correction to a diffusive growth, i.e., L(t) ~(t ln t)^{1/2}. In order to understand this behavior, we introduced a simplephenomenological model of coarsening based on the annihilation dynamics of avortex-antivortex pair, incorporating the effect of vortex inertia andlogarithmically divergent mobility of the vortex. With a suitable choice of theparameters, numerical solutions of the simple model can fit the full simulationresults very adequately. The effective growth exponent in the early time stageis larger due to the effect of the vortex inertia, which crosses over into latetime stage characterized by positive logarithmic correction to a diffusivegrowth. We also investigated the non-equilibrium autocorrelation function fromwhich the so called {\lambda} exponent can be extracted. We get {\lambda} =1.99(2) which is distinctively larger than the value of {\lambda} = 1.17 forthe purely dissipative model-A dynamics of non-conserved O(2) models.

Coarsening Kinetics of a Two Dimensional O(2) Ginzburg-Landau Model: Effect of Reversible Mode Coupling