### Schroedinger operator with non-zero accumulation points of complex eigenvalues

Analysis and Geometry Seminar

5th March 2020, 3:15 pm – 4:15 pm

Fry Building, 2.04

We consider Schroedinger operators on the whole Euclidean space or on the half-space, subject to real Robin boundary conditions. I will present the construction of a non-real potential that decays at infinity so that the corresponding Schroedinger operator has infinitely many non-real eigenvalues accumulating at every point of the essential spectrum. This proves that the Lieb-Thirring inequalities, crucial in quantum mechanics for the proof of stability of matter, do no longer hold in the non-selfadjoint case.

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