It is impossible to study a system without disturbing it by the measuring process. To determine the spectrum of a microwave billiard, for example, we have to drill a hole into its wall, introduce a wire, and radiate a microwave field. We learnt in Section 3.2.2 that the spectrum obtained for a rectangular microwave cavity is no longer integrable, but has become pseudointegrable by the presence of the antenna. The measurement thus unavoidably yields an unwanted combination of the system's own properties and those of the measuring apparatus. The mathematical tool to treat the coupling between the system and the environment is provided by scattering theory, which was originally developed in nuclear physics [Mah69, Lew91]. This theory has been successfully applied to mesoscopic systems and microwave billiards as well.

In this chapter scattering theory will be introduced with special emphasis on billiard systems. We shall also discuss the amplitude distributions of wave functions in chaotic systems, since they enter into the calculation of the distribution of scattering matrix elements. The perturbing bead method, used to get information on field distributions in microwave resonators, can also be described by scattering theory. In the last section we shall touch on the discussion of mesoscopic systems, which can be linked to scattering theory via the Landauer formula [Lan57] expressing conduction through mesoscopic devices in terms of transmission probabilities.