  We calculate the temperature dependence of the fluorescence Stokes shift and
the fluorescence decay time in linear Frenkel exciton systems resulting from
the thermal redistribution of exciton population over the band states. The
following factors, relevant to common experimental conditions, are accounted
for in our kinetic model: (weak) localization of the exciton states by static
disorder, coupling of the localized excitons to vibrations in the host medium,
a possible non-equilibrium of the subsystem of localized Frenkel excitons on
the time scale of the emission process, and different excitation conditions
(resonant or non resonant). A Pauli master equation, with microscopically
calculated transition rates, is used to describe the redistribution of the
exciton population over the manifold of localized exciton states. We find a
counterintuitive non-monotonic temperature dependence of the Stokes shift. In
addition, we show that depending on experimental conditions, the observed
fluorescence decay time may be determined by vibration-induced intra-band
relaxation, rather than radiative relaxation to the ground state. The model
considered has relevance to a wide variety of materials, such as linear
molecular aggregates, conjugated polymers, and polysilanes.
