Details
| Original language | English |
|---|---|
| Pages (from-to) | 217-232 |
| Number of pages | 16 |
| Journal | Integral Equations and Operator Theory |
| Volume | 69 |
| Issue number | 2 |
| Publication status | Published - 1 Jan 2011 |
| Externally published | Yes |
Abstract
We study spectral properties of Schrödinger operators on. ℝdThe electromagnetic potential is assumed to be determined locally by a colouring of the lattice points in ℤd, with the property that frequencies of finite patterns are well defined. We prove that the integrated density of states (spectral distribution function) is approximated by its finite volume analogues, i.e. the normalised eigenvalue counting functions. The convergence holds in the space Lp(I) where I is any finite energy interval and 1 ≤ p < ∞ is arbitrary.
Keywords
- finite local complexity, Integrated density of states, random Schrödinger operators
ASJC Scopus subject areas
- Mathematics(all)
- Analysis
- Mathematics(all)
- Algebra and Number Theory
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In: Integral Equations and Operator Theory, Vol. 69, No. 2, 01.01.2011, p. 217-232.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Lp-Approximation of the Integrated Density of States for Schrödinger Operators with Finite Local Complexity
AU - Gruber, Michael J.
AU - Lenz, Daniel H.
AU - Veselić, Ivan
PY - 2011/1/1
Y1 - 2011/1/1
N2 - We study spectral properties of Schrödinger operators on. ℝdThe electromagnetic potential is assumed to be determined locally by a colouring of the lattice points in ℤd, with the property that frequencies of finite patterns are well defined. We prove that the integrated density of states (spectral distribution function) is approximated by its finite volume analogues, i.e. the normalised eigenvalue counting functions. The convergence holds in the space Lp(I) where I is any finite energy interval and 1 ≤ p < ∞ is arbitrary.
AB - We study spectral properties of Schrödinger operators on. ℝdThe electromagnetic potential is assumed to be determined locally by a colouring of the lattice points in ℤd, with the property that frequencies of finite patterns are well defined. We prove that the integrated density of states (spectral distribution function) is approximated by its finite volume analogues, i.e. the normalised eigenvalue counting functions. The convergence holds in the space Lp(I) where I is any finite energy interval and 1 ≤ p < ∞ is arbitrary.
KW - finite local complexity
KW - Integrated density of states
KW - random Schrödinger operators
UR - http://www.scopus.com/inward/record.url?scp=78751648251&partnerID=8YFLogxK
U2 - 10.1007/s00020-010-1831-6
DO - 10.1007/s00020-010-1831-6
M3 - Article
AN - SCOPUS:78751648251
VL - 69
SP - 217
EP - 232
JO - Integral Equations and Operator Theory
JF - Integral Equations and Operator Theory
SN - 0378-620X
IS - 2
ER -