Schrödinger Operator with Non-Zero Accumulation Points of Complex Eigenvalues

Boegli, Sabine

Abstract

We study Schrödinger operators H=−Δ+V in L2(Ω) where Ω is Rd or the half-space Rd+, subject to (real) Robin boundary conditions in the latter case. For p>d we construct a non-real potential V∈Lp(Ω)∩L∞(Ω) that decays at infinity so that H has infinitely many non-real eigenvalues accumulating at every point of the essential spectrum σess(H)=[0,∞). This demonstrates that the Lieb–Thirring inequalities for selfadjoint Schrödinger operators are no longer true in the non-selfadjoint case.

Citation

Boegli, S. (2017). Schrödinger Operator with Non-Zero Accumulation Points of Complex Eigenvalues. Communications in Mathematical Physics, 352(2), 629-639. https://doi.org/10.1007/s00220-016-2806-5

• Journal Article Type: Article
• Acceptance Date: Oct 10, 2016
• Online Publication Date: Nov 18, 2016
• Publication Date: Jun 30, 2017
• Deposit Date: Dec 11, 2019
• Publicly Available Date: Dec 12, 2019
• Journal: Communications in Mathematical Physics
• Print ISSN: 0010-3616
• Electronic ISSN: 1432-0916
• Publisher: Springer
• Peer Reviewed: Peer Reviewed
• Volume: 352
• Issue: 2
• Pages: 629-639
• DOI: https://doi.org/10.1007/s00220-016-2806-5
• Public URL: https://durham-repository.worktribe.com/output/1311923