  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 short-scale.
In particular we unveil a universal crossover from exponential to power-law
ballistic-like 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.
