Nonlinear Sciences – Chaotic Dynamics
Scientific paper
2001-04-18
Adv. in Solid State Phys. 41, 459 (2001)
Nonlinear Sciences
Chaotic Dynamics
LaTeX, 12 pages, 9 figures; invited contribution to Symposium "30 Jahre Gutzwiller Spurformel" at DPG spring meeting, Hamburg,
Scientific paper
Since its first appearance in 1971, Gutzwiller's trace formula has been extended to systems with continuous symmetries, in which not all periodic orbits are isolated. In order to avoid the divergences occurring in connection with symmetry breaking and orbit bifurcations (characteristic of systems with mixed classical dynamics), special uniform approximations have been developed. We first summarize some of the recent developments in this direction. Then we present applications of the extended trace formulae to describe prominent gross-shell effects of various finite fermion systems (atomic nuclei, metal clusters, and a mesoscopic device) in terms of the leading periodic orbits of their suitably modeled classical mean-field Hamiltonians.
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