Order and Chaos in Quantum Irregular Scattering: Wigner’s Time Delay

Nearly thirty years of chaos research have shown that chaos is an ubiquitous phenomenon. Almost any dynamical system with a sufficiently large phase space described by nonlinear equations shows some kind of complexity in its time evolution, i.e. chaos. The degree of complexity is measured by topological entropy, Lyapunov exponents, decay of correlations, and, in the case of dissipative systems, various fractal dimensions. Examples abound, ranging from nonlinear oscillators to hydrodynamical systems and the motion of planets and asteroids (Schuster 1988). Nevertheless, these investigations have also revealed significant differences between an irregular looking chaotic signal and a really and truly random one, due to ‘order within chaos’ (the title of a conference, Campbell and Rose 1983, and a book, Bergé, Pomeau and Vidal 1988). One particular example of this order and coherence in chaos will be exploited below.