An exact dynamical solution to a linear chain doublet exciton with exponential memory

An exact analytic solution to the non-Markoffian spin one-half exciton linear chain system is found by diagonalising and Laplace transforming the coupled space and spin equations. As a particular example, numerical calculations of the time evolution of the two-site exciton system are presented for several realistic values of space and spin memory times. The unimportance of the cross-channel non-Markoffian behaviour for the cases where the space and spin memory times differ by at least a factor of ten is illustrated by comparison with the traditional Pauli master equation solutions. The memory can lead to oscillating populations which, on time scales shorter than or comparable with the relevant memory time, look like coherent transfer. Coherent motion can be observed, for certain values of the parameters, in the slower channel long after the more normal channel has become Markoffian. Interference regimes are possible, but require similar values of space and spin transfer integrals; this is improbable for organics.