  We quantitatively analyze the dynamics of the quantum phase distribution
associated with the reduced density matrix of a system, as the system evolves
under the influence of its environment with an energy-preserving quantum
nondemolition (QND) type of coupling. We take the system to be either an
oscillator (harmonic or anharmonic) or a two-level atom (or equivalently, a
spin-1/2 system), and model the environment as a bath of harmonic oscillators,
initially in a general squeezed thermal state. The impact of the different
environmental parameters is explicitly brought out as the system starts out in
various initial states. The results are applicable to a variety of physical
systems now studied experimentally with QND measurements.
