Coherent Wave Propagation in Multimode Systems with Correlated Noise

Imperfections in multimode systems lead to mode mixing and interferences between propagating modes. Such disorder is typically characterized by a finite correlation time (in quantum evolution) or correlation length (in paraxial evolution). We show that the long-scale dynamics of an initial excitation that spread in mode space can be tailored by the coherent dynamics on a short scale. In particular we unveil a universal crossover from exponential to power-law ballisticlike decay of the initial mode. Our results have applications to various wave physics frameworks, ranging from multimode fiber optics to quantum dots and quantum biology.