Semiclassical and weak-magnetic-field eigenvalue asymptotics for the Schrödinger operator with electromagnetic potential
George D. Raikov (1994)
Annales de l'I.H.P. Physique théorique
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George D. Raikov (1994)
Annales de l'I.H.P. Physique théorique
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László Erdős (2002)
Annales de l’institut Fourier
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We show that the lowest eigenvalue of the magnetic Schrödinger operator on a line bundle over a compact Riemann surface is bounded by the -norm of the magnetic field . This implies a similar bound on the multiplicity of the ground state. An example shows that this degeneracy can indeed be comparable with even in case of the trivial bundle.
Luca Bugliaro, Charles L. Fefferman, Gian Michele Graf (1999)
Revista Matemática Iberoamericana
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We establish a Lieb-Thirring type estimate for Pauli Hamiltonians with non-homogeneous magnetic fields. Besides of depending on the size of the field, the bound also takes into account the size of the field gradient. We then apply the inequality to prove stability of non-relativistic quantum mechanical matter coupled to the quantized ultraviolet-cutoff electromagnetic field for arbitrary values of the fine structure constant.
Heinz Siedentop, Rudi Weikard (1991)
Annales scientifiques de l'École Normale Supérieure
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Akira Iwatsuka, Hideo Tamura (1998)
Annales de l'institut Fourier
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This article studies the asymptotic behavior of the number of the negative eigenvalues as of the two dimensional Pauli operators with electric potential decaying at and with nonconstant magnetic field , which is assumed to be bounded or to decay at . In particular, it is shown that , when decays faster than under some additional conditions.