Tuesday Seminar of Analysis

Seminar information archive ~03/28Next seminarFuture seminars 03/29~

Date, time & place Tuesday 16:00 - 17:30 156Room #156 (Graduate School of Math. Sci. Bldg.)
Organizer(s) ISHIGE Kazuhiro, SAKAI Hidetaka, ITO Kenichi

2015/07/21

16:30-18:00   Room #126 (Graduate School of Math. Sci. Bldg.)
Sohei Ashida (Department of Mathematics, Kyoto University)
Born-Oppenheimer approximation for an atom in constant magnetic fields (Japanese)
[ Abstract ]
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. Martinez and Sordoni also dealt with such a case but their reduced Hamiltonian includes the vector potential terms. 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. Using the reduced evolution we also obtain the asymptotic expantion of the evolution for a specific localized initial data, which verifies the straight motion of an atom in constatnt magnetic fields.