DYNAMICS OF VORTEX NUCLEATION IN HE-3-A FLOW

Quantum phase slippage in superfluid He-3 flow is simulated numerically in rectangular slab geometries. Assuming that the flow is confined to a channel having horizontal surfaces close to each other, the spatial problem reduces to the two transverse dimensions; we report time-dependent computer simulations of superfluid He-3 flow in 2+1 dimensions using the time-dependent Ginzburg-Landau equations. The quantum-dynamic processes of phase slippage in He-3 are demonstrated to be associated with superfluid vortex nucleation; we thus confirm Anderson's assumption for phase slippage through vortex motion in superfluids. We also find several other phase-slip scenarios involving vortices, phase-slip lines, and combinations thereof for the coupled multicomponent order-parameter amplitudes. We consider both diffuse and specular boundary conditions at the side walls and demonstrate that our results are essentially independent of the boundaries. We compute the critical current for vortex nucleation as a function of the channel width, and compare it with existing theories of vortex nucleation; we also discuss our calculations in connection with experiments on phase slippage in He-3 flow. One of our most important results is that the superfluid order parameter for the vortices generated in the computer simulations does not vanish anywhere; i.e., the vortices possess superfluid core structures; hence the processes of phase slip for superfluid He-3 are nonlocal in space-time.