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

2025/01/01 by Duong, G. K., Nam, Phan Thành
#35R11 #46B70 #46E35 #81Q10 #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Mathematical Physics (math-ph) #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.2501.00866

Abstract

We prove an analogue of the Lieb--Thirring inequality for many-body quantum systems with the kinetic operator ∑_i (-Δ_i)^s and the interaction potential of the form ∑_i δ_i^-2s where δ_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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