Order and chaos in quantum irregular scattering: Wigner's time delay

Recent developments in the semiclassical analysis of chaotic systems are reviewed and illustrated for Wigner's time delay in elastic scattering of a point particle from three disks in the plane. The convergence of the cycle expanded periodic orbit expression for Wigners time delay is demonstrated. Different regimes in form factor (the Fourier transform of the two point correlation function) of the semiclassical time delay are identified and their relation to Berry's semiclassical theory of the spectral rigidity are discussed.