Scattering and bound states of quasiparticles at the A-B phase boundary of superfluid ${}_{}{}^3{}_{}{}^{}\mathrm{He}$

The boundary between the A and B phases of superfluid ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ possesses many interesting features because of the drastically different bulk order parameters. We study the transmission and Andreev reflection of ballistic wave packets of excitations incident onto the A-B phase boundary. We find that the A-B phase boundary is magnetically active and is capable of converting an unpolarized incident wave packet into transmitted and Andreev reflected wave pakets which are partially polarized. We also consider equilibrium properties due to bound states and resonances of excitations localized near the phase boundary. These states contribute to magnetic correlations and to mass and spin currents flowing in the plane of the interface.