DOI link for Concluding remarks
Concluding remarks book
The M. C. Gutzwiller trace formula has played a prominent role in the study of quantum systems whose classical analogues are chaotic. Although of measure zero in a sea of chaos in the classical phase space, the periodic orbits still open a classical window to view the quantum behavior of such systems. One of the earliest applications of the trace formula in this connection was made by Strutinsky and collaborators in their studies of deformed atomic nuclei. The same physics of the dominance of short periodic orbits in finite-sized systems makes the trace formula a powerful tool in the study of mesoscopic devices. Fascinating quantal behavior in the propagation of wave packets, like the phenomenon of recurrence, is explained by a semiclassical analysis. Diffractive orbits are specially important for grazing angles of encounter and, of course, play a leading role in scattering in the forward direction.