Semiclassical eigenvalue estimates for the Pauli operator with strong non-homogeneous magnetic fields, II. Leading order asymptotic estimates
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.
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Author
Erdös, LászlóISTA 
;
Solovej, Jan
;
Solovej, JanAbstract
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
Acknowledgement
L. E. gratefully acknowledges financial support from the Forschungsinstitut fur Mathematik, ETH, Zurich, where this work was started. He is also grateful for the hospitality and support of Aarhus University during his visits. The authors wish to thank the referee for the careful reading of the manuscript and the many helpful remarks and suggestions.
Volume
188
Issue
3
Page
599 - 656
ISSN
IST-REx-ID
Cite this
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. Springer. 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. Springer, 1997. 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. Springer, 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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