Aspects of the Quasiclassical t-Matrix Boundary Condition

We apply the t-matrix boundary conditions of Rainer to study the critical current of superfluid 3He confined to a thin channel between realistic rough surfaces using quasiclassical techniques. Rainerʹs conditions lead directly to a simple, stable and comprehensive algorithm for solving the quasiclassical equations which we present in detail. The conditions yielded physical results in all cases studied and their ease of use permitted an exhaustive search through the phase space of solutions. A robust metastable state appears for narrow channel widths suggesting the possibility of two different critical currents.