Semiclassical interference of bifurcations

Details Semiclassical interference of bifurcations Semiclassical interference of bifurcations

1997-03-03

arxiv.org/abs/chao-dyn/9703003v1

Europhys. Lett. 38, 423-428 (1997)

Nonlinear Sciences

Chaotic Dynamics

6 pages EuroLATEX (style files included), 4 figures, submitted to Europhys. Lett

Scientific paper

10.1209/epl/i1997-00262-4

In semiclassical studies of systems with mixed phase space, the neighbourhood of bifurcations of co-dimension two is felt strongly even though such bifurcations are ungeneric in classical mechanics. We discuss a scenario which reveals this fact and derive the correct semiclassical contribution of the bifurcating orbits to the trace of the unitary time evolution operator. That contribution has a certain collective character rather than being additive in the individual periodic orbits involved. The relevance of our observation is demonstrated by a numerical study of the kicked top; the collective contribution derived is found to considerably improve the semiclassical approximation of the trace.

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