Optimal Lieb-Thirring type inequalities for Schrödinger and Jacobi operators with complex potentials
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866915530947952640 |
|---|---|
| author | Bögli, Sabine Petpradittha, Sukrid |
| author_facet | Bögli, Sabine Petpradittha, Sukrid |
| contents | We prove optimal Lieb-Thirring type inequalities for Schrödinger and Jacobi operators with complex potentials. Our results bound eigenvalue power sums (Riesz means) by the $L^p$ norm of the potential, where in contrast to the self-adjoint case, each term 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(s) thereof. Our Lieb-Thirring type bounds only hold for integrable weight functions. To prove optimality, we establish divergence estimates for non-integrable weight functions. The divergence rates exhibit a logarithmic or even polynomial gain compared to semiclassical methods (Weyl asymptotics) for real potentials. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_02288 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Optimal Lieb-Thirring type inequalities for Schrödinger and Jacobi operators with complex potentials Bögli, Sabine Petpradittha, Sukrid Spectral Theory Mathematical Physics Analysis of PDEs 47B36, 34L40, 47A10, 47A75 We prove optimal Lieb-Thirring type inequalities for Schrödinger and Jacobi operators with complex potentials. Our results bound eigenvalue power sums (Riesz means) by the $L^p$ norm of the potential, where in contrast to the self-adjoint case, each term 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(s) thereof. Our Lieb-Thirring type bounds only hold for integrable weight functions. To prove optimality, we establish divergence estimates for non-integrable weight functions. The divergence rates exhibit a logarithmic or even polynomial gain compared to semiclassical methods (Weyl asymptotics) for real potentials. |
| title | Optimal Lieb-Thirring type inequalities for Schrödinger and Jacobi operators with complex potentials |
| topic | Spectral Theory Mathematical Physics Analysis of PDEs 47B36, 34L40, 47A10, 47A75 |
| url | https://arxiv.org/abs/2510.02288 |