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We experimentally investigate the lateral diffusion of dipolar excitons in coupled quantum wells in two (2D) and one (1D) dimensions. In 2D, the exciton expansion obeys non-linear temporal dynamics due to the repulsive dipole pressure at a high exciton density, in accordance with recent reports. In contrast, the observed 1D expansion behaves linearly in time even at high exciton densities. The corresponding 1D diffusion coefficient exceeds the one in 2D by far and depends linearly on the exciton density. We attribute the findings to screening of quantum well disorder by the dipolar excitons.

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