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 Itanos 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.
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