On a class of random Schrödinger operators. (English) Zbl 0578.60059
Summary: Considered are random Schrödinger operators on \(L^ 2({\mathbb{R}}^ d)\) that are stationary and metrically transitive with respect to a lattice, e.g., \(H=H_ 0+V_{\omega}\) with \(V_{\omega}(x)=\sum_{i\in Z^ d}q_ i(\omega)f(x-x_ i)\), \(\{q_ i\}\) independent, identically distributed. A method of carrying over results from the case of potentials metrically transitive with respect to \({\mathbb{R}}^ d\) is presented. Among these results are the Thouless formula and S. Kotani’s theory [Stochastic analysis, Proc. Taniguchi Int. Symp., Katata & Kyoto/Jap. 1982, North-Holland Math. Libr. 32, 225-247 (1984; Zbl 0549.60058)].
MSC:
| 60H25 | Random operators and equations (aspects of stochastic analysis) |
| 81P20 | Stochastic mechanics (including stochastic electrodynamics) |
Keywords:
random Schrödinger operatorsCitations:
Zbl 0549.60058References:
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