Early time behavior of the order parameter coupled to a conserved density: A study in a semi-infinite geometry

We study the short time behavior of the order parameter coupled to a conserved field in semi-infinite geometry. The short time exponent, obtained by solving the one loop differential equations for the conserved density and the order parameter, agrees with the prediction from a scaling argument based on short distance expansion. The scaling analysis further shows that this exponent satisfies a scaling relation similar to that known in the case of a nonconserved order parameter without any coupling.