Quantum evolution in the stroboscopic limit of repeated measurements.

We consider a quantum system dynamics caused by successive selective and nonselective measurements of the probe coupled to the system. For the finite measurement rate τ-1 and the system-probe interaction strength γ we derive analytical evolution equations in the stroboscopic limit τ→0 and γ2τ=const, which can be considered as a deviation from the Zeno subspace dynamics on a longer time scale T∼(γ2τ)-1≫γ-1. Nonlinear quantum dynamics is analyzed for selective stroboscopic projective measurements of an arbitrary rank. Nonselective measurements are shown to induce the semigroup dynamics of the system-probe aggregate. Both nonlinear and decoherent effects become significant at the time scale T∼(γ2τ)-1, which is illustrated by a number of examples. [ABSTRACT FROM AUTHOR]