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

TL;DR

This paper investigates the early time dynamics of an order parameter coupled to a conserved density in a semi-infinite system, confirming theoretical predictions through differential equation analysis and scaling arguments.

Contribution

It provides a detailed analysis of the short time behavior of coupled order parameter and conserved density, extending scaling relations to this coupled system.

Findings

Short time exponent matches scaling predictions.

Scaling relation similar to nonconserved case is satisfied.

Differential equations confirm theoretical scaling behavior.

Abstract

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.