  Using a scheme involving a lifting of a row contraction we introduce a toy
model of repeated interactions between quantum systems. In this model there is
an outgoing Cuntz scattering system involving two wandering subspaces. We
associate to this model an input/output linear system which leads to a transfer
function. This transfer function is a multi-analytic operator, and we show that
it is inner if we assume that the system is observable. Finally it is
established that transfer functions coincide with characteristic functions of
associated liftings.
