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Quantum parametric resonance

Weigert, S. (orcid.org/0000-0002-6647-3252) (2002) Quantum parametric resonance. Journal of Physics A: Mathematical and General. pp. 4169-4181. ISSN 0305-4470

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The quantum mechanical equivalent of parametric resonance is studied. A simple model of a periodically kicked harmonic oscillator is introduced which can be solved exactly. Classically stable and unstable regions in parameter space are shown to correspond to Floquet operators with qualitatively different properties. Their eigenfunctions, which are calculated exactly, exhibit a transition: for parameter values with classically stable solutions the eigenstates are normalizable while they cannot be normalized for parameter values with classically unstable solutions. Similarly, the spectrum of quasi energies undergoes a specific transition. These observations remain valid qualitatively for arbitrary linear systems exhibiting classically parametric resonance such as the paradigm example of a frequency modulated pendulum described by Mathieu's equation.

Item Type: Article
Copyright, Publisher and Additional Information: © 2002 IOP Publishing Ltd. This is an author produced version of a paper published in Journal of Physics A: Mathematical and General.
Institution: The University of York
Academic Units: The University of York > Mathematics (York)
Depositing User: Repository Officer
Date Deposited: 22 Jun 2006
Last Modified: 29 May 2016 15:12
Published Version: http://dx.doi.org/10.1088/0305-4470/35/18/312
Status: Published
Refereed: Yes
URI: http://eprints.whiterose.ac.uk/id/eprint/1349

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