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Harmonic oscillator subject to parametric pulses: an amplitude (Milne) oscillator approach

  • A harmonic oscillator subject to a parametric pulse is examined. The aim of the paper is to present a new theory for analysing transitions due to parametric pulses. The new theoretical notions which are introduced relate the pulse parameters in a direct way with the transition matrix elements. The harmonic oscillator transitions are expressed in terms of asymptotic properties of a companion oscillator, the Milne (amplitude) oscillator. A traditional phase-amplitude decomposition of the harmonic-oscillator solutions results in the so-called Milne's equation for the amplitude, and the phase is determined by an exact relation to the amplitude. This approach is extended in the present analysis with new relevant concepts and parameters for pulse dynamics of classical and quantal systems. The amplitude oscillator has a particularly nice numerical behavior. In the case of strong pulses it does not possess any of the fast oscillations induced by the pulse on the original harmonic oscillator. Furthermore, the new dynamical parameters introduced in this approach relate closely to relevant characteristics of the pulse. The relevance to quantum mechanical problems such as reflection and transmission from a localized well and mechanical problems of controlling vibrations is illustrated.

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Author:K.-E. Thylwe, H. J. Korsch
URN (permanent link):urn:nbn:de:hbz:386-kluedo-10870
Document Type:Article
Language of publication:English
Year of Completion:2001
Year of Publication:2001
Publishing Institute:Technische Universität Kaiserslautern
Date of the Publication (Server):2000/11/16
Tag:Amplitude-Phase Method; Control; Milne Equation; Parametric Excitation
Faculties / Organisational entities:Fachbereich Physik
DDC-Cassification:5 Naturwissenschaften und Mathematik / 530 Physik
Licence (German):Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011