  At total filling factor $\nu=1$ quantum Hall bilayers can have an ordered
ground state with spontaneous interlayer phase coherence. The ordered state is
signaled experimentally by dramatically enhanced interlayer tunnel conductances
at low bias voltages; at larger bias voltages inter-layer currents are similar
to those of the disordered state. We associate this change in behavior with the
existence of a critical current beyond which static inter-layer phase
differences cannot be maintained, and examine the dependence of this critical
current on sample geometry, phase stiffness, and the coherent tunneling energy
density. Our analysis is based in part on analogies between coherent bilayer
behavior and spin-transfer torque physics in metallic ferromagnets. Comparison
with recent experiments suggests that disorder can dramatically suppress
critical currents.
