  We study a general quantum system interacting with environment modeled by the
bosonic heat bath of Caldeira and Leggett type. General interaction
Hamiltonians are considered that commute with the system's Hamiltonian so that
there is no energy exchange between the system and bath. We argue that this
model provides an appropriate description of adiabatic quantum decoherence,
i.e., loss of entanglement on time scales short compared to those of thermal
relaxation processes associated with energy exchange with the bath. The
interaction Hamiltonian is then proportional to a conserved "pointer
observable." Calculation of the elements of the reduced density matrix of the
system is carried out exactly, and time-dependence of decoherence is
identified, similar to recent results for related models. Our key finding is
that the decoherence process is controlled by spectral properties of the
interaction rather than system's Hamiltonian.
