  We review results of a recently developed model of a microscopic quantum
system interacting with the macroscopic world components which are modeled by
collections of bosonic modes. The interaction is via a general operator
$\Lambda$ of the system, coupled to the creation and annihilation operators of
the environment modes. We assume that in the process of a nearly instantaneous
quantum measurement, the function of the environment involves two distinct
parts: the pointer and the bath. Interaction of the system with the bath leads
to decoherence such that the system and the pointer both evolve into a
statistical mixture state described by the density matrix such that the system
is in one of the eigenstates of $\Lambda$ with the correct quantum mechanical
probability, whereas the expectation values of pointer operators retain
amplified information on that eigenstate. We argue that this process represents
the initial step of a quantum measurement. Calculation of the elements of the
reduced density matrix of the system and pointer is carried out exactly, and
time dependence of decoherence is identified. We discuss general implications
of our model of energy-conserving coupling to a heat bath for processes of
adiabatic quantum decoherence. We also evaluate changes in the expectation
values of certain pointer operators and suggest that these can be interpreted
as macroscopic indicators of the measurement outcome.
