PACS. 03.65B -Foundations, theory of measurement, miscellaneous theories. PACS. 05.30 -Quantum statistical mechanics. PACS. 05.45 -Theory and models of chaotic systems.Abstract. -A simple model for the coupling of a quantum system to a macroscopic measuring device is proposed, which allows to describe continuous measurements with finite time resolution. It is used to derive a quantum map, generating the dynamics of the quantum kicked rotor under the influence of continuous measurements. Numerical experiments with this quantum map show that the incoherent back-action of the measuring device always destroys dynamical localization on a sufficiently long time scale, and renders the measured dynamics diffusive.
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