Decoherence and Localization in Quantum Two - Level

We study and compare the decoherent histories approach, the environment-induced decoherence and the localization properties of the solutions to the stochastic Schrr odinger equation in quantum jump simulation and quantum state diiusion approaches, for a quantum two-level system model. We show, in particular, that there is a close connection between the decoherent histories and the quantum jump simulation, complementing a connection with the quantum state diiusion approach noted earlier by Dii osi, Gisin, Halliwell and Percival. In the case of the decoherent histories analysis, the degree of approximate decoherence is discussed in detail.