Some Remarks on the Theory of Trapping of Excitons in the Photosynthetic Unit

The problem of random motion of an exciton in a square lattice with a sink is formulated in terms of finite difference equations. The case where the exciton suffers a fixed delay time at each lattice site is solved numerically. The more realistic case, also investigated by Knox [J. Theoret. Biol. 21, 244 (1968)], where this delay time is inversely proportional to the number of nearest neighbors, is shown to be equivalent to the case with periodic boundary conditions. Consequently, an exact analytic expression for the total delay time can for that case be derived. For lattices of any size this quantity can now easily be calculated. Giving the exciton the possibility of escaping from the lattice will influence the total delay time. This effect is investigated, as well as the effect of distributing the sink over the lattice sites. As a by‐product, an amusingly simple formula $$\mathrm{k(\lambda )-}\frac{1}{\mathrm{c(\lambda )}}{\displaystyle \sum _{\mu }}\mathrm{c(\mu )}$$ is derived for the average path length upon first return in a random walk over an arbitrary network.