  A new approach to the modeling of nonfree particle diffusion is presented.
The approach uses a general setup based on geometric graphs (networks of
curves), which means that particle diffusion in anything from arrays of
barriers and pore networks to general geometric domains can be considered and
that the (free random walk) central limit theorem can be generalized to cover
also the nonfree case. The latter gives rise to a continuum-limit description
of the diffusive motion where the effect of partially absorbing barriers is
accounted for in a natural and non-Markovian way that, in contrast to the
traditional approach, quantifies the absorptivity of a barrier in terms of a
dimensionless parameter in the range 0 to 1. The generalized theorem gives two
general analytic expressions for the continuum-limit propagator: an infinite
sum of Gaussians and an infinite sum of plane waves. These expressions entail
the known method-of-images and Laplace eigenfunction expansions as special
cases and show how the presence of partially absorbing barriers can lead to
phenomena such as line splitting and band gap formation in the plane wave
wave-number spectrum.
