Zeno effect and ergodicity in finite-time quantum measurements

We demonstrate that an attempt to measure a nonlocal in time quantity, such as the time average < A >(T) of a dynamical variable A, by separating Feynman paths into ever narrower exclusive classes traps the system in eigensubspaces of the corresponding operator (A) over cap. Conversely, in a long measurement of < A >(T) to a finite accuracy, the system explores its Hilbert space and is driven to a universal steady state in which the von Neumann ensemble average of (A) over cap coincides with < A >(T). Both effects are conveniently analyzed in terms of singularities and critical points of the corresponding amplitude distribution and the Zeno-like behavior is shown to be a consequence of the conservation of probability.