Expansion of the almost sure spectrum in the weak disorder regime

Abstract

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 ${\ell }^2({\mathbb{Z}}^d)$.

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Cited by in corpus (2)

• Expansion of the spectrum in the weak disorder regime for random operators in continuum space
• Quantum Hamiltonians with weak random abstract perturbation. II. Localization in the expanded spectrum