We consider the Schrödinger operator with Poisson type random potential, and derive the spectrum which is deterministic almost surely. Apart from some exceptional cases, the spectrum is equal to [0, ∞) if the single-site potential is nonnegative, and is equal to R if the negative part of it does not vanish with positive probability, which is consistent with the naive observation. To prove that, we use the theory of admissible potential and the Weyl asymptotics. Communicated by Jean Bellissard.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Nuclear and High Energy Physics
- Mathematical Physics