Chennai Mathematical Institute


11.00 a.m.
The spectrum of Schr\"odinger operators with Poisson type random potential
(joint work with Kazunori Ando, Akira Iwatsuka and Fumihiko Nakano)

Masahiro Kaminaga
Institute of Mathematical Sciences, Chennai.


We consider the Schr\"odinger 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 $[0, \infty)$ if the single-site potential is non-negative, and is equal to ${\bf R}$ 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.