Coarsening of binary Bose superfluids: an effective theory

We derive an effective equation of motion for binary Bose mixtures, which generalizes the Cahn-Hilliard description of classical binary fluids to superfluid systems. Within this approach, based on a microscopic Hamiltonian formulation, we show that the domain growth law $L(t)\sim t^{2/3}$ observed in superfluid mixtures is not driven by hydrodynamic flows, but arises from the competition between interactions and quantum pressure. The effective theory allows us to derive key properties of superfluid coarsening, including domain growth and Porod's laws. This provides a new theoretical framework for understanding phase separation in superfluid mixtures.