Duke Mathematical Journal

Semiclassical eigenvalue estimates for the Pauli operator with strong nonhomogeneous magnetic fields, I: Nonasymptotic Lieb-Thirring–type estimate

László Erdös and Jan Philip Solovej
Source: Duke Math. J. Volume 96, Number 1 (1999), 127-173.
First Page: Show Hide

Related Works:

Primary Subjects: 81Q10
Secondary Subjects: 47A10, 47F05, 47N50
Full-text: Access denied (no subscription detected)
We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber.
If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text
Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077228944
Mathematical Reviews number (MathSciNet): MR1663923
Zentralblatt MATH identifier: 01425171
Digital Object Identifier: doi:10.1215/S0012-7094-99-09604-7

References

[AHS] J. Avron, I. Herbst, and B. Simon, Schrödinger operators with magnetic fields. I. General interactions, Duke Math. J. 45 (1978), no. 4, 847–883.
Mathematical Reviews (MathSciNet): MR80k:35054
Zentralblatt MATH: 0399.35029
Digital Object Identifier: doi:10.1215/S0012-7094-78-04540-4
Project Euclid: euclid.dmj/1077313102
[B] L. Bugliaro, C. Fefferman, J. Fröhlich, G. M. Graf, and J. Stubbe, A Lieb-Thirring bound for a magnetic Pauli Hamiltonian, Comm. Math. Phys. 187 (1997), no. 3, 567–582.
Mathematical Reviews (MathSciNet): MR98i:81044
Zentralblatt MATH: 0998.47049
Digital Object Identifier: doi:10.1007/s002200050149
[C] H. L. Cycon, R. G. Froese, W. Kirsch, and B. Simon, Schrödinger operators with application to quantum mechanics and global geometry, Texts and Monographs in Physics, Springer-Verlag, Berlin, 1987.
Mathematical Reviews (MathSciNet): MR88g:35003
Zentralblatt MATH: 0619.47005
[E1] László Erdős, Ground-state density of the Pauli operator in the large field limit, Lett. Math. Phys. 29 (1993), no. 3, 219–240.
Mathematical Reviews (MathSciNet): MR95a:81080
Zentralblatt MATH: 0850.81030
Digital Object Identifier: doi:10.1007/BF00761110
[E2] László Erdős, Magnetic Lieb-Thirring inequalities, Comm. Math. Phys. 170 (1995), no. 3, 629–668.
Mathematical Reviews (MathSciNet): MR96i:81069
Zentralblatt MATH: 0843.47040
Digital Object Identifier: doi:10.1007/BF02099152
Project Euclid: euclid.cmp/1104273255
[ES] László Erdős and Jan Philip Solovej, Semiclassical eigenvalue estimates for the Pauli operator with strong non-homogeneous magnetic fields. II. Leading order asymptotic estimates, Comm. Math. Phys. 188 (1997), no. 3, 599–656.
Mathematical Reviews (MathSciNet): MR2001b:81028
Zentralblatt MATH: 0909.47052
Digital Object Identifier: doi:10.1007/s002200050181
[F] Charles Fefferman, Stability of Coulomb systems in a magnetic field, Proc. Nat. Acad. Sci. U.S.A. 92 (1995), no. 11, 5006–5007.
Mathematical Reviews (MathSciNet): MR96m:81261
Zentralblatt MATH: 0826.35101
Digital Object Identifier: doi:10.1073/pnas.92.11.5006
[FLL] Jürg Fröhlich, Elliott H. Lieb, and Michael Loss, Stability of Coulomb systems with magnetic fields. I. The one-electron atom, Comm. Math. Phys. 104 (1986), no. 2, 251–270.
Mathematical Reviews (MathSciNet): MR88a:81023a
Zentralblatt MATH: 0595.35098
Digital Object Identifier: doi:10.1007/BF01211593
Project Euclid: euclid.cmp/1104115002
[HNW] B. Helffer, J. Nourrigat, and X. P. Wang, Sur le spectre de l'équation de Dirac (dans $\bf R\sp 3$ ou $\bf R\sp 2$) avec champ magnétique, Ann. Sci. École Norm. Sup. (4) 22 (1989), no. 4, 515–533.
Mathematical Reviews (MathSciNet): MR91e:35155
Zentralblatt MATH: 0703.35127
[I] Victor Ivrii, Microlocal analysis and precise spectral asymptotics, Springer Monographs in Mathematics, Springer-Verlag, Berlin, 1998.
Mathematical Reviews (MathSciNet): MR99e:58193
Zentralblatt MATH: 0906.35003
[L] Elliott H. Lieb, The number of bound states of one-body Schroedinger operators and the Weyl problem, Geometry of the Laplace operator (Proc. Sympos. Pure Math., Univ. Hawaii, Honolulu, Hawaii, 1979), Proc. Sympos. Pure Math., XXXVI, Amer. Math. Soc., Providence, R.I., 1980, pp. 241–252.
Mathematical Reviews (MathSciNet): MR82i:35134
Zentralblatt MATH: 0445.58029
[LLS] Elliott H. Lieb, Michael Loss, and Jan Philip Solovej, Stability of matter in magnetic fields, Phys. Rev. Lett. 75 (1995), no. 6, 985–989.
Mathematical Reviews (MathSciNet): MR96j:81142
Zentralblatt MATH: 1020.81957
Digital Object Identifier: doi:10.1103/PhysRevLett.75.985
[LSY1] Elliott H. Lieb, Jan Philip Solovej, and Jakob Yngvason, Asymptotics of heavy atoms in high magnetic fields. II. Semiclassical regions, Comm. Math. Phys. 161 (1994), no. 1, 77–124.
Mathematical Reviews (MathSciNet): MR95f:81103
Zentralblatt MATH: 0807.47058
Digital Object Identifier: doi:10.1007/BF02099414
Project Euclid: euclid.cmp/1104269793
[LSY2] E. H. Lieb, J. P. Solovej, and J. Yngvason, Ground states of large quantum dots in magnetic fields, Phys. Rev. B 51 (1995), 10646–10665.
Mathematical Reviews (MathSciNet): MR1721312
Zentralblatt MATH: 0929.35126
[LT] E. H. Lieb and W. Thirring, “A bound on the moments of the eigenvalues of the Schrödinger Hamiltonian and their relation to Sobolev inequalities”, Studies in Mathematical Physics: Essays in Honor of Valentine Bargmann eds. E. H. Lieb, B. Simon, and A. Wightman, Princeton University Press, Princeton, 1976, pp. 269–303.
Zentralblatt MATH: 0342.35044
[LY] Michael Loss and Horng-Tzer Yau, Stabilty of Coulomb systems with magnetic fields. III. Zero energy bound states of the Pauli operator, Comm. Math. Phys. 104 (1986), no. 2, 283–290.
Mathematical Reviews (MathSciNet): MR88a:81023c
Zentralblatt MATH: 0607.35083
Digital Object Identifier: doi:10.1007/BF01211595
Project Euclid: euclid.cmp/1104115004
[MR] Michael Melgaard and Gregory V. Rozenblum, Spectral estimates for magnetic operators, Math. Scand. 79 (1996), no. 2, 237–254.
Mathematical Reviews (MathSciNet): MR98f:81067
Zentralblatt MATH: 0888.35074
[S1] A. Sobolev, Asymptotic behavior of the energy levels of a quantum particle in a homogeneous magnetic field perturbed by a decreasing electric field, J. Soviet Math. 35 (1986), 2201–2212.
Zentralblatt MATH: 0643.35028
[S2] Alexander V. Sobolev, On the Lieb-Thirring estimates for the Pauli operator, Duke Math. J. 82 (1996), no. 3, 607–635.
Mathematical Reviews (MathSciNet): MR97e:81030
Zentralblatt MATH: 0882.47056
Digital Object Identifier: doi:10.1215/S0012-7094-96-08225-3
Project Euclid: euclid.dmj/1077245254
[S3] Alexander V. Sobolev, Lieb-Thirring inequalities for the Pauli operator in three dimensions, Quasiclassical methods (Minneapolis, MN, 1995), IMA Vol. Math. Appl., vol. 95, Springer, New York, 1997, pp. 155–188.
Mathematical Reviews (MathSciNet): MR98i:81047
Zentralblatt MATH: 0889.35086
[So] S. N. Solnyshkin, Asymptotic behavior of the energy of bound states of the Schrödinger operator in the presence of electric and homogeneous magnetic fields, Spectral theory. Wave processes, Probl. Mat. Fiz., vol. 10, Leningrad. Univ., Leningrad, 1982, 266–278, 302.
Mathematical Reviews (MathSciNet): MR84f:81098
Zentralblatt MATH: 0513.35012

2012 © Duke University Press

Duke Mathematical Journal

Duke Mathematical Journal

Turn MathJax Off
What is MathJax?