Semiclassical eigenvalue estimates for the Pauli operator with strong non-homogeneous magnetic fields, II. Leading order asymptotic estimates

L. Erdös, J. Solovej, Communications in Mathematical Physics 188 (1997) 599–656.

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Abstract
We give the leading order semiclassical asymptotics for the sum of the negative eigenvalues of the Pauli operator (in dimension two and three) with a strong non-homogeneous magnetic field. As in [LSY-II] for homogeneous field, this result can be used to prove that the magnetic Thomas-Fermi theory gives the leading order ground state energy of large atoms. We develop a new localization scheme well suited to the anisotropic character of the strong magnetic field. We also use the basic Lieb-Thirring estimate obtained in our companion paper [ES-I].
Publishing Year
Date Published
1997-10-01
Journal Title
Communications in Mathematical Physics
Volume
188
Issue
3
Page
599 - 656
IST-REx-ID

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Erdös L, Solovej J. Semiclassical eigenvalue estimates for the Pauli operator with strong non-homogeneous magnetic fields, II. Leading order asymptotic estimates. Communications in Mathematical Physics. 1997;188(3):599-656. doi:10.1007/s002200050181
Erdös, L., & Solovej, J. (1997). Semiclassical eigenvalue estimates for the Pauli operator with strong non-homogeneous magnetic fields, II. Leading order asymptotic estimates. Communications in Mathematical Physics, 188(3), 599–656. https://doi.org/10.1007/s002200050181
Erdös, László, and Jan Solovej. “Semiclassical Eigenvalue Estimates for the Pauli Operator with Strong Non-Homogeneous Magnetic Fields, II. Leading Order Asymptotic Estimates.” Communications in Mathematical Physics 188, no. 3 (1997): 599–656. https://doi.org/10.1007/s002200050181.
L. Erdös and J. Solovej, “Semiclassical eigenvalue estimates for the Pauli operator with strong non-homogeneous magnetic fields, II. Leading order asymptotic estimates,” Communications in Mathematical Physics, vol. 188, no. 3, pp. 599–656, 1997.
Erdös L, Solovej J. 1997. Semiclassical eigenvalue estimates for the Pauli operator with strong non-homogeneous magnetic fields, II. Leading order asymptotic estimates. Communications in Mathematical Physics. 188(3), 599–656.
Erdös, László, and Jan Solovej. “Semiclassical Eigenvalue Estimates for the Pauli Operator with Strong Non-Homogeneous Magnetic Fields, II. Leading Order Asymptotic Estimates.” Communications in Mathematical Physics, vol. 188, no. 3, Springer, 1997, pp. 599–656, doi:10.1007/s002200050181.

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