Expansion of the almost sure spectrum in the weak disorder regime

The spectrum of random ergodic Schrödinger-type operators is almost surely a deterministic subset of the real line. The random operator can be considered as a perturbation of a periodic one. As soon as the disorder is switched on via a global coupling constant, the spectrum expands. We estimate how much the spectrum expands at its bottom for operators on ℓ²(ℤᵈ).

Subjects

Almost sure spectrum

Expansion of the spectrum

Weak disorder

Mathematical Physics

Mathematics - Mathematical Physics

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Expansion of the almost sure spectrum in the weak disorder regime