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Decoherence of a quantum system (which then starts to display classicalfeatures) results from the interaction of the system with the environment, andis well described in the framework of the theory of continuous quantummeasurements (CQM). Reviewed are the various approaches to the CQM theory, andthe approach based on the effective complex Hamiltonians is discussed ingreater detail. The effective complex Hamiltonian is derived from therestricted path integral, which emphasizes the role of information in thedynamics of the system being measured. The complex Hamiltonian is used foranalyzing the CQM of energy in a two-level system. Such measurement isdemonstrated to be capable of monitoring the quantum transition, and the backeffect of monitoring on the probability of transition is analyzed. Therealization of this type of measurement by a long series of soft observationsof the system is presented.Comment: 55 pages, latex, 4 figures in EP

Decoherence and the theory of continuous quantum measurements