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arXiv · 2501.00866

Lieb--Thirring inequalities for large quantum systems with inverse nearest-neighbor interactions

G. K. Duong·Phan Thành Nam
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Abstract

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.

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BibTeXRIS

G. K. Duong, Phan Thành Nam. 2025-01-01. Lieb--Thirring inequalities for large quantum systems with inverse nearest-neighbor interactions. https://arxiv.org/abs/2501.00866

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