Born–Oppenheimer Approximation for an Atom in Constant Magnetic Fields

We obtain a reduction scheme for the study of the quantum evolution of an atom in constant magnetic fields using the method developed by Martinez, Nenciu and Sordoni based on the construction of almost invariant subspace. In Martinez and Sordoni (Mem AMS 936, 2009 ) such a case is also studied but t...

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Bibliographic Details
Published inAnnales Henri Poincaré Vol. 17; no. 8; pp. 2173 - 2197
Main Author Ashida, Sohei
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.08.2016
Springer Nature B.V
Subjects
Asymptotic series
Classical and Quantum Gravitation
Dynamical Systems and Ergodic Theory
Elementary Particles
Evolution
Invariants
Magnetic fields
Mathematical and Computational Physics
Mathematical Methods in Physics
Physics
Physics and Astronomy
Quantum Field Theory
Quantum Physics
Relativity Theory
Theoretical
Semiclassical Limit
Invariant Subspace
Symbol Class
Zeroth Order Term
Quantum Evolution
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Summary:We obtain a reduction scheme for the study of the quantum evolution of an atom in constant magnetic fields using the method developed by Martinez, Nenciu and Sordoni based on the construction of almost invariant subspace. In Martinez and Sordoni (Mem AMS 936, 2009 ) such a case is also studied but their reduced Hamiltonian includes the vector potential terms. In this paper, using the center of mass coordinates and constructing the almost invariant subspace different from theirs, we obtain the reduced Hamiltonian which does not include the vector potential terms of the nucleus. Using the reduced evolution, we also obtain the asymptotic expansion of the evolution for a specific localized initial data, which verifies the straight motion of an atom in constant magnetic fields.
ISSN:1424-0637
1424-0661
DOI:10.1007/s00023-016-0458-9