CLASSICAL HAMILTONIAN DESCRIPTION OF A 2-LEVEL QUANTUM SYSTEM - THE QUANTUM ZENO EFFECT

We consider the simplest quantum system, namely the two-level system w ith real matrix elements, and exhibit its specific phase properties re lated to the complex Hamiltonian formalism provided by a simple canoni cal transformation between the Schroedinger equation and a classical d ynamical system that actually describes the dynamics of a spin 1/2. In the case of the quantum Zeno effect, it yields the provocative theore tical suggestion and experimental prediction that an energy measuremen t should always yield the same energy value (which is either the upper or the lower energy level, depending on the value of the energy expec tation value), contrary to the standard quantum rule stating that an e nergy measurement should share the probabilities between the two energ y levels (except for the eigenstates). This makes a quasi-continuously observed two-level quantum system very similar to a classical system from the point of view of energy measurements. (C) 1998 Elsevier Scien ce B.V.