Growth Kinetics for a System with Conserved Order Parameter: Off Critical Quenches

The theory of growth kinetics developed previously is extended to the asymmetric case of off-critical quenches for systems with a conserved scalar order parameter. In this instance the new parameter $M$, the average global value of the order parameter, enters the theory. For $M=0$ one has critical quenches, while for sufficiently large $M$ one approaches the coexistence curve. For all $M$ the theory supports a scaling solution for the order parameter correlation function with the Lifshitz-Slyozov-Wagner growth law $L \sim t^{1/3}$. The theoretically determined scaling function depends only on the spatial dimensionality $d$ and the parameter $M$, and is determined explicitly here in two and three dimensions. Near the coexistence curve oscillations in the scaling function are suppressed. The structure factor displays Porod's law $Q^{-(d+1)}$ behaviour at large scaled wavenumbers $Q$, and $Q^{4}$ behaviour at small scaled wavenumbers, for all $M$. The peak in the structure factor widens as $M$ increases and develops a significant tail for quenches near the coexistence curve. This is in qualitative agreement with simulations.