Propagators weakly associated to a family of Hamiltonians and the adiabatic theorem for the Landau Hamiltonian with a time-dependent Aharonov-Bohm flux
Asch, J. ; Hradecky, I. ; Stovicek, P.
arXiv, 0502030 / Harvested from arXiv
Text on arXiv
We study the dynamics of a quantum particle moving in a plane under the influence of a constant magnetic field and driven by a slowly time-dependent singular flux tube through a puncture. The known adiabatic results do not cover these models as the Hamiltonian has time dependent domain. We give a meaning to the propagator and prove an adiabatic theorem. To this end we introduce and develop the new notion of a propagator weakly associated to a time-dependent Hamiltonian.
Publié le : 2005-02-08
Classification:  Mathematical Physics,  35Q40, 35J10, 81V45 
@article{0502030,
     author = {Asch, J. and Hradecky, I. and Stovicek, P.},
     title = {Propagators weakly associated to a family of Hamiltonians and the
  adiabatic theorem for the Landau Hamiltonian with a time-dependent
  Aharonov-Bohm flux},
     journal = {arXiv},
     volume = {2005},
     number = {0},
     year = {2005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0502030}
}

Asch, J.; Hradecky, I.; Stovicek, P. Propagators weakly associated to a family of Hamiltonians and the
  adiabatic theorem for the Landau Hamiltonian with a time-dependent
  Aharonov-Bohm flux. arXiv, Tome 2005 (2005) no. 0, . http://gdmltest.u-ga.fr/item/0502030/