Volume 38, Number 6, May III 1997
|423 - 428
|01 September 2002
Semiclassical interference of bifurcations
Fachbereich Physik, Universität-Gesamthochschule Essen - D-45117 Essen, Germany
Accepted: 17 April 1997
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.
PACS: 05.45.+b – Theory and models of chaotic systems / 03.65.Sq – Semiclassical theories and applications / 03.20.+i – Classical mechanics of discrete systems: general mathematical aspects
© EDP Sciences, 1997
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