Waves in a rapidly varying random potential: A numerical study

Abstract

We study the time evolution of a wave packet in a rapidly varying (in time) random potential. We find that the wave function becomes ``multifractal,'' i.e., that an infinite number of exponents is needed to describe its evolution. The width of the packet is found to increase as \ensuremath{\surd}t , i.e., diffusively. The evolution of the center of mass is compatible with a subdiffusive ${\mathit{t}}^{1/4}$ law.