Decomposition of the instantaneous spectrum of a random system

We characterize the nature of the instantaneous spectrum of a random system. We define the instantaneous spectrum as the Wigner spectrum of the state of the system, and we apply a method which transforms the system in the domain of the Wigner spectrum. By using this approach we prove that the instantaneous spectrum is made by three components. Two components decay with time, while a third stationary component is reached for large times.