Adiabatic Theorem without a Gap Condition
Avron, J. E. ; Elgart, A.
arXiv, 9805022 / Harvested from arXiv
Text on arXiv
We prove the adiabatic theorem for quantum evolution without the traditional gap condition. All that this adiabatic theorem needs is a (piecewise) twice differentiable finite dimensional spectral projection. The result implies that the adiabatic theorem holds for the ground state of atoms in quantized radiation field. The general result we prove gives no information on the rate at which the adiabatic limit is approached. With additional spectral information one can also estimate this rate.
Publié le : 1998-05-25
Classification:  Mathematical Physics,  Mathematics - Spectral Theory,  Physics - Atomic Physics,  Quantum Physics 
@article{9805022,
     author = {Avron, J. E. and Elgart, A.},
     title = {Adiabatic Theorem without a Gap Condition},
     journal = {arXiv},
     volume = {1998},
     number = {0},
     year = {1998},
     language = {en},
     url = {http://dml.mathdoc.fr/item/9805022}
}

Avron, J. E.; Elgart, A. Adiabatic Theorem without a Gap Condition. arXiv, Tome 1998 (1998) no. 0, . http://gdmltest.u-ga.fr/item/9805022/