Lieb-Thirring-type inequalities for random Schr\"odinger operators with complex potentials
Jean-Claude Cuenin, Konstantin Merz
TL;DR
This paper reviews eigenvalue bounds for random Schrödinger operators with complex potentials and introduces new Schatten norm estimates to improve bounds on eigenvalue sums.
Contribution
It provides new Schatten norm estimates for the resolvent and applies them to derive improved eigenvalue bounds for complex-valued potentials.
Findings
New Schatten norm estimates for the resolvent
Enhanced bounds for sums of eigenvalues
Comprehensive review of eigenvalue bounds for complex potentials
Abstract
We review some results and proofs on eigenvalue bounds for random Schr\"odinger operators with complex-valued potentials. We also include new Schatten norm estimates for the resolvent and use them to obtain bounds for sums of eigenvalues.
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Taxonomy
TopicsSpectral Theory in Mathematical Physics · Numerical methods in inverse problems