Optimal Lieb-Thirring type inequalities for Schrödinger operators with complex potentials

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• Sukrid Petpradittha (Durham University)
• Thursday 05 February 2026, 15:00-15:15
• Seminar Room 1, Newton Institute.

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GSTW05 - Emerging Horizons in Geometric Spectral Theory: an ECRs workshop

The purpose of this talk is to present optimal Lieb-Thirring type inequalities for Schrödinger operators with complex potentials. Lieb-Thirring inequalities for complex potentials bound eigenvalue power sums (Riesz means) by the Lp norm of the potential, where in contrast to the selfadjoint case, each summand needs to be weighted by a function of the ratio of the distance of the eigenvalue to the essential spectrum and the distance to the endpoint thereof. These Lieb-Thirring type bounds hold only for integrable weight functions. To prove optimality, the divergence estimates for non-integrable weight functions are established. The divergence rates exhibit a logarithmic or even polynomial gain compared to semiclassical methods (Weyl asymptotics) for real potentials. This is joint work with Sabine Boegli (Durham).

This talk is part of the Isaac Newton Institute Seminar Series series.

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