Decay and Computability
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.
KeywordsHilbert Space Hamiltonian System Constant Ratio Selfadjoint Operator Decay State
Unable to display preview. Download preview PDF.
- 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
- Antoniou, I., Shkarin, S.A.: Decay spectrum and decay subspace of normal operators. J Edinburg Math. Soc. (in press).Google Scholar
- Salem, R.: Algebraic numbers and Fourier analysis. Reprint. Orig. publ. 1963 by Heath, Boston. The Wadsworth Mathematics Series, Belmont, California 1983.Google Scholar
- Weidmann, H.: Linear Operators in Hilbert space. Springer Verlag 1980.Google Scholar
- Antoniou, I., Suchanecki, Z.: Quantum systems with fractal spectra. Chaos Soli-tons and Fractals - Special Volume (submitted).Google Scholar