  If unitary evolution of a quantum system is interrupted by a sequence of
measurements we call the dynamics as quantum Zeno dynamics. We show that under
quantum Zeno dynamics not only the transition probability (leading to quantum
Zeno effect) but also phases are affected. We call this new effect as quantum
Zeno phase effect (QZPE) which says that under repeated measurements the
geometric phase of a quantum system can be inhibited. Since geometric phase
attributes a memory to a quatum system this result also proves that under
quantum Zeno dynamics the memory of a system can be erased. We have proposed a
neutron interference experiment where this prediction can be tested. We also
beleive that with Itano's kind of set up for two-level systems this prediction
can be tested. This will provide a new way of controlling phase shift in
interference experiment by doing repeated measurements.
