  I present the exact solution of a toy model for gravitationally induced
decoherence. The toy model has Hamiltonian resembling optomechanical systems.
It is an oscillator system coupled through its energy to an oscillator heat
bath. I find the decoherence effect of vacuum fluctuations at zero temperature.
Also for a finite bath I show that the decoherence is in general present and
the system does not return to its initial coherence unless the fundamental
frequencies of the bath have rational ratios.
