On the continuous spectral component of the Floquet operator for a periodically kicked quantum system

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dc.creatorMcCaw, J. M.
dc.creatorMcKellar, B. H. J.
dc.date2005-06-01
dc.date2005-10-25
dc.date.accessioned2026-07-07T06:42:16Z
dc.date.available2026-07-07T06:42:16Z
dc.descriptionBy a straightforward generalisation, we extend the work of Combescure from rank-1 to rank-N perturbations. The requirement for the Floquet operator to be pure point is established and compared to that in Combescure. The result matches that in McCaw. The method here is an alternative to that work. We show that if the condition for the Floquet operator to be pure point is relaxed, then in the case of the delta-kicked Harmonic oscillator, a singularly continuous component of the Floquet operator spectrum exists. We also provide an in depth discussion of the conjecture presented in Combescure of the case where the unperturbed Hamiltonian is more general. We link the physics conjecture directly to a number-theoretic conjecture of Vinogradov and show that a solution of Vinogradov's conjecture solves the physics conjecture. The result is extended to the rank-N case. The relationship between our work and the work of Bourget on the physics conjecture is discussed.
dc.description25 pages, published in Journal of Mathematical Physics
dc.identifierhttps://arxiv.org/abs/math-ph/0506001
dc.identifierhttp://arxiv.org/abs/math-ph/0506001
dc.identifierJournal of Mathematical Physics 46, 103503 (2005)
dc.identifierdoi:10.1063/1.2035027
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/101973
dc.subjectMathematical Physics
dc.titleOn the continuous spectral component of the Floquet operator for a periodically kicked quantum system
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