Dynamics of excitonic photoluminescence (PL) lineshape in narrow G a A s single quantum w e l l s is investigated by measuring transient PL spectra in t h e picosecond time domains under direct excitation. W e obtain distinct spectroscopic evidences for the exciton center-of-mass motion by drift-diffusion towards the I& potential minima caused by t h e well-width fluctuations. That is, dynamical Stokes-shifts are directly observed. W e find t h a t inhomogeneous potential fluctuations in t h e

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... uantum w e l l plane r e s u l t in asymmetry of t h e PL lineshape. The exciton trapped by tlje I-m i n i m a formed due t o t h e spatial inhomogeneity is directly evidenced by t h e Lineshape analysis. From c o mparison w i t h a case of spatially coherent quantum w e l l s w i t h growth island terraces, excellent correlation is obtained between the dynamical lineshape and t h e microscopic details of a t o m i c w e heterointerfaces.