Discontinuities of the Integrated Density of States for Random Operators on Delone Sets

Communications in Mathematical Physics

Volumn 241, Issue 2-3, 2003, Pages 235-243

  Klassert, Steffen ^a   Lenz, Daniel ^a   Stollmann, Peter ^a  

^a CHEMNITZ UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0242370757     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00220-003-0920-7     Document Type: Article

References (16)

1. [ATF] Aral, M., Tokihiro, T., Fujiwara, T.: Strictly localized states on a two-dimensional Penrose lattice. Phys. Rev. B 38, 1621-1626 (1988)
2. [BSJ] Baake, M., Schlottmann, M., Jarvis, P.D.: Quasiperiodic tilings with tenfold symmetry and equivalence with respect to local derivability. J. Phys. A 24, 4637-4654 (1991)
3. [BLT] Bellissard, J., Lima, R., Testard, D.: Almost Periodic Schrödinger Operators. In: Mathematics + physics. Vol. 1, Singapore: World Sci. Publishing, 1995, pp. 1-64
4. [FATK] Fujiwara, T., Arai, M., Tokihiro, T., Kohmoto, M.: Localized states and self-similar states of electrons on a two-dimensional Penrose lattice. Phys. Rev. B 37, 2797-2804 (1988)
5. [H] Hof, A.: A remark on Schrödinger operators on aperiodic tilings. J. Statist. Phys. 81, 851-855 (1996)
6. [K] Kellendonk, J.: Noncommutative geometry of tilings and gap labelling. Rev. Math. Phys. 7, 1133-1180 (1995)
7. [KS] Kohmoto, M., Sutherland, B.: Electronic States on a Penrose Lattice. Phys. Rev. Lett 56, 2740-2743 (1986)
8. [KF] Krajčí, M., Fujiwara, T.: Strictly localized eigenstates on a three-dimensional Penrose lattice. Phys. Rev. B 38, 12903-12907 (1988)
9. [Len] Lenz, D.: Uniform ergodic theorems on subshifts over a finite alphabet. Ergodic theory & Dynamical systems 22, 245-255 (2002)
10. [LS1] Lenz, D., Stollmann, P.: Quasicrystals, aperiodic order, and groupoid von Neumann algebras. C.R. Acad. Sci. Paris, Ser. I 334, 1131-1136 (2002)
11. [LS2] Lenz, D., Stollmann, P.: Delone dynamical systems and associated random operators. To appear in Proc. DAMP, Constanta 2001, eprint: arXiv math-ph/0202142
12. [LS3] Lenz, D., Stollmann, P.: An ergodic theorem for Delone dynamical systems and existence of the density of states. In preparation
13. [LS4] Lenz, D., Stollmann, P.: Algebras of Random Operators associated to Delone dynamical systems. To appear in Math. Phys. Analysis and Geometry, eprint: math-ph/0210031
14. [SA] Schenker, J.H., Aizenman, M.: The creation of spectral gaps by graph decoration. Lett. Math. Phys. 53, 253-262 (2000)
15. [Sol1] Solomyak, B.: Dynamics of self-similar tilings. Ergodic Theory Dynam. Systems 17, 695-738 (1997)
16. [Sol2] Solomyak, B: Spectrum of dynamical systems arising from Delone sets. In: Proceedings of Workshop on Aperiodic Order, Patera, J., (ed.), Fields Inst. Monographs, Providence. RI: Amer. Math. Soc., 1998