  The inhibition of the decay of a quantum system by frequent measurements is
known as quantum Zeno effect. Beyond the limit of projective measurements, the
interplay between the unitary dynamics of the system and the coupling to a
measurement apparatus becomes relevant. We explore this interplay by
considering a quantum particle moving on a one-dimensional chain. A local
measurement by coupling to an apparatus with a two-dimensional Hilbert space
detects the presence of the particle on a specific chain site. The decay of the
population is studied analytically for a two-site chain and numerically for a
larger system as a function of the measurement time and the time between
subsequent measurements. Particular attention is given to the shift of the
energy of the measured site due to the coupling to the apparatus. The decay of
the initial population can be hindered or accelerated, depending on the chosen
system and the coupling parameters.
