Lieb--Thirring inequalities for large quantum systems with inverse nearest-neighbor interactions
| Autor: | Duong, G. K., Nam, Phan Thành |
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| Rok vydání: | 2025 |
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| Druh dokumentu: | Working Paper |
| Popis: | We prove an analogue of the Lieb--Thirring inequality for many-body quantum systems with the kinetic operator $\sum_i (-\Delta_i)^s$ and the interaction potential of the form $\sum_i \delta_i^{-2s}$ where $\delta_i$ is the nearest-neighbor distance to the point $x_i$. Our result extends the standard Lieb--Thirring inequality for fermions and applies to quantum systems without the anti-symmetry assumption on the wave functions. Additionally, we derive similar results for the Hardy--Lieb--Thirring inequality and obtain the asymptotic behavior of the optimal constants in the strong coupling limit. Comment: 27 pages |
| Databáze: | arXiv |
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