The Josephson effect under particle-number restriction is investigated base
d on the Feynman two-state model. The existence of new dynamical states of
the Josephson phase inherent in such a restricted situation is shown. The n
ew state describes a number of features recently observed in a superfluid H
e-3 weak-link system. Quantum decay from Josephson pi states is also invest
igated. Since the pi state has two different decay paths, they can interfer
e during the decay processes by quantum tunneling due to a topological phas
e originating from total particle-number restriction, and result in a parit
y effect for tunneling. (C) 1999 Academic Press.