  Coupling the output of a source quantum system into a target quantum system
is easily treated by cascaded systems theory if the intervening quantum channel
is dispersionless. However, dispersion may be important in some transfer
protocols, especially in solid-state systems. In this paper we show how to
generalize cascaded systems theory to treat such dispersion, provided it is not
too strong. We show that the technique also works for fermionic systems with a
low flux, and can be extended to treat fermionic systems with large flux. To
test our theory, we calculate the effect of dispersion on the fidelity of a
simple protocol of quantum state transfer. We find good agreement with an
approximate analytical theory that had been previously developed for this
example.
