Wegner Estimate and Disorder Dependence for Alloy-Type Hamiltonians with Bounded Magnetic Potential
Abstrak
We consider non-ergodic magnetic random Schrödinger operators with a bounded magnetic vector potential. We prove an optimal Wegner estimate valid at all energies. The proof is an adaptation of arguments from Klein (Commun Math Phys 323(3):1229–1246, 2013), combined with a recent quantitative unique continuation estimate for eigenfunctions of elliptic operators from Borisov et al. (J Math Phys, arXiv:1512.06347 [math.AP]). This generalizes Klein’s result to operators with a bounded magnetic vector potential. Moreover, we study the dependence of the Wegner-constant on the disorder parameter. In particular, we show that above the model-dependent threshold $$E_0(\infty ) \in (0, \infty ]$$E0(∞)∈(0,∞], it is impossible that the Wegner-constant tends to zero if the disorder increases. This result is new even for the standard (ergodic) Anderson Hamiltonian without magnetic field.
Topik & Kata Kunci
Penulis (2)
Matthias Täufer
Martin Tautenhahn
Akses Cepat
- Tahun Terbit
- 2017
- Bahasa
- en
- Total Sitasi
- 8×
- Sumber Database
- Semantic Scholar
- DOI
- 10.1007/s00023-017-0640-8
- Akses
- Open Access ✓