  We investigate the dynamics of two quantum mechanical oscillator system-bath
toy models obtained by truncating to zero spatial dimensions linearized gravity
coupled to a massive scalar field and scalar QED. The scalar-gravity toy model
maps onto the phase damped oscillator, while the scalar QED toy model
approximately maps onto an oscillator system subject to two-photon damping. The
toy models provide potentially useful insights into solving for open system
quantum dynamics relevant to the full scalar QED and weak gravitational field
systems, in particular operational probes of the decoherence for initial scalar
field system superposition states.
