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We consider a point particle in one dimension initially confined to a finitespatial region whose state is frequently monitored by projection operators ontothat region. In the limit of infinitely frequent monitoring, the state neverescapes from the region -- this is the Zeno effect. The aim of this paper is toshow how the Zeno effect disappears in the classical limit in this and similarexamples. We give a general argument showing that the Zeno effect is suppressedin the presence of a decoherence mechanism which kills interference betweenhistories. We show how this works explicitly by coupling to a decoheringenvironment. Smoothed projectors are required to give the problem properdefinition and this implies the existence of a momentum cutoff. We show thatthe escape rate from the region approaches the classically expected result, andhence the Zeno effect is suppressed, as long as the environmentally-inducedfluctuations in momentum are sufficiently large and we establish the associatedtimescale. We link our results to earlier work on the hbar -->0 limit of theZeno effect. We illustrate our results by plotting the probability flux linesfor the density matrix (which are equivalent to Bohm trajectories in the purestate case). These illustrate both the Zeno and anti-Zeno effects very clearly,and their suppression. Our results are closely related to our earlier paperdemonstrating the suppression of quantum-mechanical reflection by decoherence

Classical Limit of the Quantum Zeno Effect by Environmental Decoherence