The Lieb–Thirring Inequality for Interacting Systems in Strong-Coupling Limit

@article{Kgler2020TheLI,
title={The Lieb–Thirring Inequality for Interacting Systems in Strong-Coupling Limit},
author={Kevin K{\"o}gler and Phan Th{\a}nh Nam},
journal={arXiv: Mathematical Physics},
year={2020}
}`
• Published 8 June 2020
• Mathematics
• arXiv: Mathematical Physics
We consider an analogue of the Lieb-Thirring inequality for quantum systems with homogeneous repulsive interaction potentials, but without the antisymmetry assumption on the wave functions. We show that in the strong-coupling limit, the Lieb-Thirring constant converges to the optimal constant of the one-body Gagliardo-Nirenberg interpolation inequality without interaction.
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References

SHOWING 1-10 OF 42 REFERENCES

Lieb-Thirring Inequality for a Model of Particles with Point Interactions

• Physics
• 2012
We consider a model of quantum-mechanical particles interacting via point interactions of infinite scattering length. In the case of fermions we prove a Lieb-Thirring inequality for the energy, i.e.,

Lieb–Thirring inequalities for wave functions vanishing on the diagonal set

• Mathematics
Annales Henri Lebesgue
• 2021
We propose a general strategy to derive Lieb-Thirring inequalities for scale-covariant quantum many-body systems. As an application, we obtain a generalization of the Lieb-Thirring inequality to wave

Fractional Hardy–Lieb–Thirring and Related Inequalities for Interacting Systems

• Mathematics
• 2015
We prove analogues of the Lieb–Thirring and Hardy–Lieb–Thirring inequalities for many-body quantum systems with fractional kinetic operators and homogeneous interaction potentials, where no

Lieb-Thirring Bounds for Interacting Bose Gases

• Physics
• 2015
We study interacting Bose gases and prove lower bounds for the kinetic plus interaction energy of a many-body wave function in terms of its particle density. These general estimates are then applied

Local Exclusion and Lieb–Thirring Inequalities for Intermediate and Fractional Statistics

• Mathematics
• 2013
In one and two spatial dimensions there is a logical possibility for identical quantum particles different from bosons and fermions, obeying intermediate or fractional (anyon) statistics. We consider

On Lieb-Thirring Inequalities for Schrödinger Operators with Virtual Level

• Mathematics
• 2006
We consider the operator H=−Δ−V in L2(ℝd), d≥3. For the moments of its negative eigenvalues we prove the estimate Similar estimates hold for the one-dimensional operator with a Dirichlet condition at

The Lieb–Thirring inequality revisited

• Mathematics
Journal of the European Mathematical Society
• 2018
We provide new estimates on the best constant of the Lieb-Thirring inequality for the sum of the negative eigenvalues of Schr\"odinger operators, which significantly improve the so far existing

Hardy and Lieb-Thirring Inequalities for Anyons

• Mathematics
• 2013
We consider the many-particle quantum mechanics of anyons, i.e. identical particles in two space dimensions with a continuous statistics parameter $${\alpha \in [0, 1]}$$α∈[0,1] ranging from bosons

Connection Between the Lieb-Thirring Conjecture for Schrödinger Operators and An Isoperimetric Problem for Ovals on the Plane

To determine the sharp constants for the one dimensional Lieb– Thirring inequalities with exponent γ ∈ (1/2, 3/2) is still an open problem. According to a conjecture by Lieb and Thirring the sharp