Europhys. Lett, 38 (6), pp. 423-428 (1997)
Semiclassical interference of bifurcations
Fachbereich Physik, Universität-Gesamthochschule Essen - D-45117 Essen, Germany
(received 6 March 1997; accepted 17 April 1997)
PACS. 05.45 - Theory and models of chaotic systems.
PACS. 03.65Sq - Semiclassical theories and applications.
PACS. 03.20 - Classical mechanics of discrete systems: general mathematical aspects.
Abstract:In semiclassical studies of systems with a 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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