On the continuous spectral component of the Floquet operator for a periodically kicked quantum system
- School of Physics, Research Centre for High Energy Physics, University of Melbourne, Victoria, 3010 (Australia)
By a straightforward generalization, we extend the work of Combescure [J. Stat. Phys. 59, 679 (1990)] 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 and McKeller [J. Math. Phys. 46, 032108 (2005)]. 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 the work of Combescure of the case where the unperturbed Hamiltonian is more general. We link the physics conjecture directly to a number-theoretic conjecture of Vinogradov [The Method of Trigonometrical Sums in the Theory of Numbers (Interscience, London, 1954)] 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 [J. Math. Anal. Appl. 276, 28 (2002); 301, 65 (2005)], on the physics conjecture is discussed.
- OSTI ID:
- 20699512
- Journal Information:
- Journal of Mathematical Physics, Vol. 46, Issue 10; Other Information: DOI: 10.1063/1.2035027; (c) 2005 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
- Country of Publication:
- United States
- Language:
- English
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