Auto-correlation functions at large times

This chapter deals with auto-correlation functions. The flexibility of the chain model is quite transparent already at its starting point. The studied problem can be specified in two major ways. One, in which both the initial state |Φ₀) and the dynamical operator Ω^ are explicitly given, as is the case in, e.g. quantum mechanics. Second, in which neither |Φ₀) or Ω^ is known, but instead the matrix elements of Φ^ or U^ are available. The chapter presents a fast method of computing the auto-correlation functions and this should be of particular importance for systems displaying detailed structures over a long period of time, as is actually the case with, e.g. the ozone photodissociation process and many other collisional systems. In this way, explicit propagations of a wave packet to very large times are avoided,.