Decay and Computability

  • I. Antoniou
  • Z. Suchanecki
Part of the International Society for Analysis, Applications and Computation book series (ISAA, volume 10)


We study Hamiltonians with singular spectra of Cantor type with a constant ratio of dissection and present strict connections between the decay properties of states and the algebraic number theory as well as the computability of decaying and non decaying states.


Hilbert Space Hamiltonian System Constant Ratio Selfadjoint Operator Decay State 


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  1. [1]
    Antoniou, I., Suchanecki, Z.: Spectral characterization of decay in quantum mechanics. Trends in Quantum Mechanics, eds. H.-D. Doebner, S.T. Ali, M. Keyl and R.F. Werner, 158–166, World Scientific, Singapore 2000.Google Scholar
  2. [2]
    Antoniou, I., Shkarin, S.A.: Decay spectrum and decay subspace of normal operators. J Edinburg Math. Soc. (in press).Google Scholar
  3. [3]
    Salem, R.: Algebraic numbers and Fourier analysis. Reprint. Orig. publ. 1963 by Heath, Boston. The Wadsworth Mathematics Series, Belmont, California 1983.Google Scholar
  4. [4]
    Weidmann, H.: Linear Operators in Hilbert space. Springer Verlag 1980.Google Scholar
  5. [5]
    Bellisard, J.: Schrödinger operators with almost periodic potential: an overview. Lect. Notes on Phys. 153 (1982), 356–363.CrossRefGoogle Scholar
  6. [6]
    Antoniou, I., Suchanecki, Z.: Quantum systems with fractal spectra. Chaos Soli-tons and Fractals - Special Volume (submitted).Google Scholar
  7. [7]
    Stewart, I.N., Tall, D.O.: Algebraic Number Theory. Chapman and Hall, London 1979.MATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2003

Authors and Affiliations

  • I. Antoniou
    • 1
    • 2
  • Z. Suchanecki
    • 1
    • 2
    • 3
  1. 1.International Solvay Institute for Physics and ChemistryBrusselsBelgium
  2. 2.Theoretische NatuurkundeFree University of BrusselsBelgium
  3. 3.Institute of MathematicsUniversity of OpolePoland

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