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We study transitions of a particle between two wells, separated by areservoir, under the condition that the particle is not detected in thereservoir. Conventional quantum trajectory theory predicts that such no-resultcontinuous measurement would not affect these transitions. We demonstrate thatit holds only for Markovian reservoirs (infinite bandwidth $\Lambda$). In thecase of finite $\Lambda$, the probability of the particle's interwelltransition is a function of the ratio $\Lambda/\nu$, where $\nu$ is thefrequency of measurements. This scaling tells us that in the limit$\nu\to\infty$, the measurement freezes the initial state (the quantum Zenoeffect), whereas for $\Lambda\to\infty$ it does not affect the particle'stransition across the reservoir. The scaling is proved analytically by derivinga simple formula, which displays two regimes, with the Zeno effect and withoutthe Zeno effect. It also supports a simple explanation of the Zeno effectentirely in terms of the energy-time uncertainty relation, with no explicit useof the projection postulate. Experimental tests of our predictions arediscussed.

Quantum transfer through a non-Markovian environment under frequent measurements and Zeno effect