Poisson local eigenvalue statistics for continuum random Schrödinger operators
Date
Tuesday, March 26, 2019 16:30 - 17:30
Speaker
Adrian Dietlein (IST Austria)
Location
Big Seminar room Ground floor / Office Bldg West (I21.EG.101)
Series
Seminar/Talk
Tags
Mathematics and CS Seminar, mathematical_seminar_ics
Host
M. Beiglböck, N. Berestycki, L. Erdös, J. Maas
Contact
Poissonian local eigenvalue statistics are believed to be a characteristic feature of spectrally localized quantum mechanical systems. For localized random Schrdinger operators Poissonian level statistics have however only been proven for the lattice Anderson model and close relatives: The proof of a key ingredient, the Minami estimate, crucially relied on the rank-1 character of the single-site potential.
We present a more flexible approach towards Minamis estimate, which for instance works at the bottom of the spectrum of a continuum random Schrdinger operator with sufficiently regular single-site distributions. The talk is based on joint work with Alex Elgart.