 Researchers in quantum chaology have focused on universal statistical properties that are independent of the quantum systems under investigation. Furthermore, studies focus on so-called simple quantum systems (i.e., those that can be described by a finite number of parameters or finite amount of information). The kinds of statistical properties studied in such systems include the statistics of energy levels and semi-classical structures of wave functions. These statistical properties are relevant for quantum state transitions, ionization and other quantum phenomena found in atomic and nuclear physics, solid state physics of mesoscopic systems and even quantum information. Some typical systems studied are quantum billiards (particles restricted to two-dimensional motions), the quantum kicked rotor, a single periodically driven spin and coupled spins. Often, iterated maps are used in investigating quantum chaos just as in classical chaos (§1.2.5 above). 