  We present an analytical study of state transfer in a spin chain in the
presence of an inhomogeneous set of exchange coefficients. We initially
consider the homogeneous case and describe a method to obtain the energy
spectrum of the system. Under certain conditions, the state transfer time can
be predicted by taking into account the energy gap between the two lowest
energy eigenstates. We then generalize our approach to the inhomogeneous case
and show that including a barrier in the chain can lead to a reduction of the
state transfer time. We additionally extend our analysis to the case of
multiple barriers. These advances may contribute to the understanding of spin
transfer dynamics in long chains where connections between neighboring spins
can be manipulated.
