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Decay and computability. (English) Zbl 1232.81021
Begehr, Heinrich G.W. (ed.) et al., Analysis and applications–ISAAC 2001. Proceedings of the 3rd international congress, Berlin, Germany, August 20–25, 2001. Dordrecht: Kluwer Academic Publishers (ISBN 1-4020-1384-1/hbk). Int. Soc. Anal. Appl. Comput. 10, 1-6 (2003).
Summary: 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.
For the entire collection see [Zbl 1031.35002].
##### MSC:
 81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis 47N50 Applications of operator theory in the physical sciences 81U05 $$2$$-body potential quantum scattering theory