  In a series of recent papers we have used an operatorial technique to
describe stock markets and, in a different context, {\em love affairs} and
their time evolutions. The strategy proposed so far does not allow any dumping
effect. In this short note we show how, within the same framework, a strictly
non periodic or quasi-periodic effect can be introduced in the model by
describing in some details a linear Alice-Bob love relation with damping.
