Magnetic Lieb-Thirring inequalities with optimal dependence on the field strength

L. Erdös, J. Solovej, Journal of Statistical Physics 116 (2004) 475–506.

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Abstract
The Pauli operator describes the energy of a nonrelativistic quantum particle with spin in a magnetic field and an external potential. Bounds on the sum of the negative eigenvalues are called magnetic Lieb-Thirring (MLT) inequalities. The purpose of this paper is twofold. First, we prove a new MLT inequality in a simple way. Second, we give a short summary of our recent proof of a more refined MLT inequality(8) and we explain the differences between the two results and methods. The main feature of both estimates, compared to earlier results, is that in the large field regime they grow with the optimal (first) power of the strength of the magnetic field. As a byproduct of the method, we also obtain optimal upper bounds on the pointwise density of zero energy eigenfunctions of the Dirac operator.
Publishing Year
Date Published
2004-08-01
Journal Title
Journal of Statistical Physics
Volume
116
Issue
1-4
Page
475 - 506
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Erdös L, Solovej J. Magnetic Lieb-Thirring inequalities with optimal dependence on the field strength. Journal of Statistical Physics. 2004;116(1-4):475-506. doi:10.1023/B:JOSS.0000037216.45270.1d
Erdös, L., & Solovej, J. (2004). Magnetic Lieb-Thirring inequalities with optimal dependence on the field strength. Journal of Statistical Physics, 116(1–4), 475–506. https://doi.org/10.1023/B:JOSS.0000037216.45270.1d
Erdös, László, and Jan Solovej. “Magnetic Lieb-Thirring Inequalities with Optimal Dependence on the Field Strength.” Journal of Statistical Physics 116, no. 1–4 (2004): 475–506. https://doi.org/10.1023/B:JOSS.0000037216.45270.1d.
L. Erdös and J. Solovej, “Magnetic Lieb-Thirring inequalities with optimal dependence on the field strength,” Journal of Statistical Physics, vol. 116, no. 1–4, pp. 475–506, 2004.
Erdös L, Solovej J. 2004. Magnetic Lieb-Thirring inequalities with optimal dependence on the field strength. Journal of Statistical Physics. 116(1–4), 475–506.
Erdös, László, and Jan Solovej. “Magnetic Lieb-Thirring Inequalities with Optimal Dependence on the Field Strength.” Journal of Statistical Physics, vol. 116, no. 1–4, Springer, 2004, pp. 475–506, doi:10.1023/B:JOSS.0000037216.45270.1d.

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