Quantum description of classical apparatus: Zeno effect and decoherence

We study the measurement process by treating classical detectors entirely quantum mechanically. As a generic model we use a point-contact detector coupled to an electron in a quantum dot and tunneling into the continuum. Transition to the classical description and the mechanism of decoherence are investigated. We concentrate on the influence of the measurement on the electron decay rate to the continuum. We demonstrate that the Zeno (or the anti-Zeno) effect requires a nonuniform density of states in the continuum. In this case we show that the anti-Zeno effect relates only to the average decay rate, whereas for sufficiently small time the Zeno effect always takes place. We discuss the experimental consequences of our results and the role of the projection postulate in a measurement process.