Dynamics of a quantum particle in a random potential

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Abstract
The motion of a quantum particle in a random potential with short‐range fluctuations is analyzed using a generalized mode‐coupling approximation. The original theory of Götze was extended by introducing a wave‐vector dependent current relaxation kernel. Here we apply the theory to the special case of exciton dynamics in a binary molecular crystal. We find a localization–delocalization transition in three dimensions with a critical exponent of 1 for the inverse localization length. In the intermediate time regime, our theory predicts a region of anomalous diffusion. This can be interpreted as a precursor to localization. At the transition point it leads to the known asymptotic low‐frequency behaviour D″(ω) α ω1/3.