Abstract
The coherent-potential approximation (CPA) is extended to describe satisfactorily the motion of particles in a random potential which is spatially correlated and smoothly varying. In contrast to existing cluster-CPA methods, the present scheme preserves the simplicity of the conventional CPA but leads to a momentum and frequency-dependent self-energy. Its accuracy is checked by a comparison with the exact moments of the Green's function and with the spectral function from numerical simulations. The scheme is applied to excitonic absorption spectra in different spatial dimensions.
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