Quantum mechanical diffusion in complex surroundings - Mizutori, Shoujirou; Åberg, Sven (Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, 1997)
The dynamics of a classical, heavy system coupled to a quantum mechanical light system is studied in a simple time-dependent random matrix model, where the degree of complexity can be changed by a “chaoticity parameter.” It is shown that the energy of the quantum mechanical system diffuses as it interacts with the classical system, providing it is chaotic, while a ballistic behavior appears in the ordered case. The energy diffusion of the chaotic system saturates, and it is shown that the saturation time is related to short-range correlations in the energy spectrum. In mixed systems the propagation of energy changes from a ballistic to diffusive behavior at a time related to long-range energy correlations.