We propose and exactly solve a model of interface growth. The model is applicable to Kardar-Parisi-Zhang type interfaces growing into an environment whose density decreases exponentially with height. We find that the average height of the interface grows as ln(t) for all spatial dimensions d. The interface width has a much richer dependence on d, showing a nontrivial crossover behavior around d=2.
|Number of pages||3|
|Journal||Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics|
|Publication status||Published - Apr 1994|