The results of photoluminescence, time-resolved photoluminescence, photoluminescence excitation and photoluminescence kinetics studies are presented for a Al_{0.3}Ga_{0.7}As/GaAs quantum well system grown without growth interruptions at the interfaces. The time-resolved photoluminescence measurements show drift of excitons towards lower energy states induced in a quantum well by potential fluctuations. We present also a first direct evidence for migration of free excitons from the 24 to 25 ML regions of the quantum well and interpret these results within a linear rate model, deriving the transition rate of 290 ps^{-1}. Such inter-island migration processes have been observed till now only in growth interrupted structures.
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