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On Computability of Decaying and Nondecaying States in Quantum Systems with Cantor Spectra

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Abstract

We study Hamiltonians with singular spectra of Cantor type with a constant ratio of dissection. The decay properties of the states in such systems depend on the nature of the dissection rate that can be characterized in terms of the algebraic number theory. We show that in spite of simplicity of the considered model the computational modeling of nondecaying states is in general impossible.

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Authors and Affiliations

  1. International Solvay Institute for Physics and Chemistry, CP 231, ULB Campus Plaine, Brussels, Belgium

    I. Antoniou

  2. Theoretische Natuurkunde, Free University of Brussels, Belgium

    I. Antoniou & Z. Suchanecki

  3. Institute of Mathematics, University of Opole, Poland

    Z. Suchanecki

Authors
  1. I. Antoniou
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  2. Z. Suchanecki
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Antoniou, I., Suchanecki, Z. On Computability of Decaying and Nondecaying States in Quantum Systems with Cantor Spectra. International Journal of Theoretical Physics 42, 2255–2263 (2003). https://doi.org/10.1023/B:IJTP.0000005957.63539.de

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  • DOI: https://doi.org/10.1023/B:IJTP.0000005957.63539.de

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