Uniform lieb-thirring inequality for the three-dimensional Pauli operator with a strong non-homogeneous magnetic field

Annales Henri Poincare

Volumn 5, Issue 4, 2004, Pages 671-741

  Erdos, László ^a   Solovej, Jan Philip ^b  

^a UNIVERSITY OF MUNICH   (Germany)

^b UNIVERSITY OF COPENHAGEN   (Denmark)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 4243137164     PISSN: 14240637     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00023-004-0180-x     Document Type: Review

References (27)

1. [AMN] C. Adam, B. Muratori and C. Nash, Multiple zero modes of the Dirac operator in three dimensions, Phys. Rev. D (3) 62, no. 8, 085026 (2000).
2. [BE] A. Balinsky, W.D. Evans, On the zero modes of Pauli operators, J. Funct. Anal. 179(1), 120-135 (2001).
3. [BFFGS] L. Bugliaro, C. Fefferman, J. Fröhlich, G.M. Graf and J. Stubbe, A Lieb-Thirring bound for a magnetic Pauli Hamiltonian, Commum. Math. Phys. 187, 567-582 (1997).
4. [BFrG] L. Bugliaro, J. Fröhlich, and G.M. Graf, Stability of quantum electrodynamics with nonrelativistic matter, Phys. Rev. Lett. 77, 3494-3497 (1996).
5. [BFG] L. Bugliaro, C. Fefferman and G.M. Graf, A Lieb-Thirring bound for a magnetic Pauli Hamiltonian, II, Rev. Mat. Iberoamericana 15, 593-619 (1999).
6. [El-1] D. Elton, New examples of zero modes, J. Phys. A 33 (41), 7297-7303 (2000).
7. [El-2] D. Elton, The local structure of zero mode producing magnetic potentials, Commun. Math. Phys. 229, 121-139 (2002).
8. [E-93] L. Erdos, Ground state density of the Pauli operator in the large field limit, Lett. Math. Phys. 29, 219-240 (1993).
9. [E-1995] L. Erdos, Magnetic Lieb-Thirring inequalities, Commun. Math. Phys. 170, 629-668 (1995).
10. [ES-I] L. Erdos and J.P. Solovej, Semiclassical eigenvalue estimates for the Pauli operator with strong non-homogeneous magnetic fields. I. Non-asymptotic Lieb-Thirring type estimate, Duke J. Math. 96, 127-173 (1999).
11. [ES-II] L. Erdos and J.P. Solovej, Semiclassical eigenvalue estimates for the Pauli operator with strong non-homogeneous magnetic fields. II. Leading order asymptotic estimates, Commun. Math. Phys. 188, 599-656 (1997).
12. 3, Rev. Math. Phys. 13 No. 10, 1247-1280 (2001).
13. [ES-IV] L. Erdos and J.P. Solovej, Magnetic Lieb-Thirring inequalities with optimal dependence on the field strength, Accepted to J. Statis. Phys. (2003). Available at http://xxx.lanl.gov/pdf/math-ph/0306066.
14. e série t. 22, 515-533 (1989).
15. [LLS] E.H. Lieb, M. Loss and J.P. Solovej, Stability of Matter in Magnetic Fields, Phys. Rev. Lett. 75, 985-989 (1995).
16. [LSY-I] E.H. Lieb, J.P. Solovej and J. Yngvason, Asymptotics of heavy atoms in high magnetic fields: I. Lowest Landau band region, Commun. Pure Appl. Math. 47, 513-591 (1994).
17. [LSY-II] E.H. Lieb, J.P. Solovej and J. Yngvason, Asymptotics of heavy atoms in high magnetic fields: II. Semiclassical regions, Commun. Math. Phys. 161, 77-124 (1994).
18. [LT1] E.H. Lieb, W. Thirring, Inequalities for moments of the eigenvalues of the Schrödinger Hamiltonian and their relation to Sobolev inequalities. In: Studies in Mathematical Physics (E. Lieb, B. Simon, A. Wightman eds.) Princeton University Press, 269-330 (1975).
19. [LY] M. Loss and H.-T. Yau, Stability of Coulomb systems with magnetic fields: III. Zero energy bound states of the Pauli operator, Commun. Math. Phys. 104, 283-290 (1986).
20. [S79] B. Simon, Functional Integration and Quantum Physics, Academic Press, New York, 1979.
21. [Sh] Z. Shen, On the moments of negative eigenvalues for the Pauli operator, J. Diff. Eq. 149, 292-327 (1998) and 151, 420-455 (1999).
22. [Sh] Z. Shen, On the moments of negative eigenvalues for the Pauli operator, J. Diff. Eq. 149, 292-327 (1998) and 151, 420-455 (1999).
23. [Sob-86] A. Sobolev, Asymptotic behavior of the energy levels of a quantum particle in a homogeneous magnetic field, perturbed by a decreasing electric field, J. Sov. Math. 35, 2201-2212 (1986).
24. [Sob-96] A. Sobolev, On the Lieb-Thirring estimates for the Pauli operator, Duke Math. J. 82, 607-635 (1996).
25. [Sob-97] A. Sobolev, Lieb-Thirring inequalities for the Pauli operator in three dimensions, IMA Vol. Math. Appl. 95, 155-188 (1997).
26. [Sob-98] A. Sobolev, Quasiclassical asymptotics for the Pauli operator, Commun. Math. Phys. 194, 109-134 (1998).
27. [Sol] S.N. Solnyshkin, The asymptotic behavior of the energy of bound states of the Schrödinger operator in the presence of electric and magnetic fields, Probl. Mat. Fiz. 10, 266-278 (1982).