TY - JOUR
T1 - Eigenvalue statistics for Schrödinger operators with random point interactions on R d, d = 1, 2, 3
AU - Hislop, Peter D.
AU - Kirsch, Werner
AU - Krishna, M.
N1 - Publisher Copyright:
© 2020 Author(s).
PY - 2020/9/1
Y1 - 2020/9/1
N2 - We prove that the local eigenvalue statistics at energy E in the localization regime for Schrödinger operators with random point interactions on Rd, for d = 1, 2, 3, is a Poisson point process with the intensity measure given by the density of states at E times the Lebesgue measure. This is one of the first examples of Poisson eigenvalue statistics for the localization regime of multi-dimensional random Schrödinger operators in the continuum. The special structure of resolvent of Schrödinger operators with point interactions facilitates the proof of the Minami estimate for these models.
AB - We prove that the local eigenvalue statistics at energy E in the localization regime for Schrödinger operators with random point interactions on Rd, for d = 1, 2, 3, is a Poisson point process with the intensity measure given by the density of states at E times the Lebesgue measure. This is one of the first examples of Poisson eigenvalue statistics for the localization regime of multi-dimensional random Schrödinger operators in the continuum. The special structure of resolvent of Schrödinger operators with point interactions facilitates the proof of the Minami estimate for these models.
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U2 - 10.1063/5.0002885
DO - 10.1063/5.0002885
M3 - Article
AN - SCOPUS:85092401341
SN - 0022-2488
VL - 61
JO - Journal of Mathematical Physics
JF - Journal of Mathematical Physics
IS - 9
M1 - 092103
ER -