On computability of decaying and nondecaying states in quantum systems with Cantor spectra

International Journal of Theoretical Physics

Volumn 42, Issue 10, 2003, Pages 2255-2263

  Antoniou, I ^a,b   Suchanecki, Z ^b,c  

^a INTERNATIONAL SOLVAY INSTITUTES   (Belgium)

^b VRIJE UNIVERSITEIT BRUSSEL   (Belgium)

^c UNIVERSITY OF OPOLE   (Poland)

Author keywords

Computability; Decay; Quantum system; S number; Singular spectrum

Indexed keywords

EID: 3843054443     PISSN: 00207748     EISSN: None     Source Type: Journal    
DOI: 10.1023/B:IJTP.0000005957.63539.de     Document Type: Article

References (17)

1. Antoniou, I., Gadella M., and Suchanecki, Z. (1998). General properties of the Liouville operator, International Journal of Theoretical Physics 37, 1641-1654.
2. Antoniou, I., Shkarin, S., and Suchanecki, Z. (1999). The spectrum of the Liouville-von Neumann operator in the Hilbert-Schmidt space. Journal of Mathematical Physics 40, 4106-4118.
3. Antoniou, I. and Shkarin, S. A. (2001). Decay spectrum and decay subspace of normal operators. Proceedings of the Royal Society Edinburg 131A, 1257-1273.
4. Antoniou, I. and Suchanecki, Z. (2000). Spectral characterization of decay in quantum mechanics. In Trends in Quantum Mechanics, Doebner, H.-D., Ali, S. T., Keyl, M., and Werner, R. F. eds., World Scientific, Singapore, pp. 158-166.
5. Antoniou, I. and Suchanecki, Z. (2002). Quantum systems with fractal spectra, Chaos Solitons and Fractals 14, 799-807.
6. Avron, J. and Simon, B. (1981a). Almost periodic Schrödinger operators, Communications in Mathematical Physics 82, 101-120.
7. Avron, J. and Simon, B. (1981b). Transient and recurrent spectrum. J. Funct. Anal. 43, 1-31.
8. Bellisard, J. (1982). Schrödinger operators with almost periodic potential: an overview, Lecture Notes in Physics 153, 356-363.
9. Damanik, D., Killip, R., and Lenz, D. (2000). Uniform spectral properties of one-dimensional quasicrystals, III. α-continuity, Communications in Mathematical Physics 212, 191-204.
10. del Rio, R., Jitomirskaya, S., Makarov N., and Simon, B. (1994). Singular continuous spectrum is generic, Bulletin of the American Mathematical Society 31, 208-212.
11. Jitomirskaya, S. and Simon, B. (1994). Operators with singular continuous spectrum: III. Almost periodic Schrödinger operators. Communications in Mathematical Physics 165, 201-205.
12. Pearson, D. B. (1978). Singular continuous measures in scattering theory, Communications in Mathematical Physics 60, 13-36.
13. Salem, R. (1983). Algebraic Numbers and Fourier Analysis. The Wadsworth Mathematics Series, Belmont, CA. (Reprint. Orig. publ. 1963 by Heath, Boston).
14. Stewart, I. N. and Tall D. O. (1979). Algebraic Number Theory, Chapman and Hall, London.
15. von Neumann, J. (1955). Mathematical Foundations of Quantum Mechanics, Princeton University Press, Princeton, NJ.
16. Weidmann, H. (1980). Linear Operators in Hilbert Space, Springer-Verlag, Berlin.
17. Zygmund, A. (1968). Trigonometric Series, Vols. I, II Cambridge University Press, Cambridge, UK.