Semiclassical Physics

Semiclassical Physics emphasizes the close connection between the shorter classical periodic orbits, and the partially resolved quantum fluctuations in the level density and response of an autonomous finite quantum system. Particular care is taken to present a detailed derivation of Gutzwillers trace formula, and its extensions to continuous symmetries, zeta function techniques, and diffractive orbits. } Semiclassical Physics emphasizes the close connection between the shorter classical periodic orbits, and the partially resolved quantum fluctuations in the level density and response of an autonomous finite quantum system. Particular care is taken to present a detailed derivation of Gutzwillers trace formula, and its extensions to continuous symmetries, zeta function techniques, and diffractive orbits. Simple model examples are used to illustrate the formalism. The self-consistent mean-field approach to the many-body problem is used, and the extended Thomas-Fermi model posited for the average properties of finite fermion systems. Strutinskys energy theorem is exploited to bring out the quantum effects in interacting systems.
Experimental manifestations of quantum shell structure, and their understanding in terms of a few classical orbits, are illustrated in atomic nuclei, metal clusters, and mesoscopic devices. Chapters one, two, and eight are meant for the general reader interested in semiclassical physics and a survey of relevant experiments. The other five chapters give a detailed, but elementary, exposition of the theory aimed at the second-year graduate student level. }