Time Development of Exponentially Small Non-Adiabatic Transitions
Hagedorn, George A. ; Joye, Alain
arXiv, 0309012 / Harvested from arXiv
Text on arXiv
Optimal truncations of asymptotic expansions are known to yield approximations to adiabatic quantum evolutions that are accurate up to exponentially small errors. In this paper, we rigorously determine the leading order non--adiabatic corrections to these approximations for a particular family of two--level analytic Hamiltonian functions. Our results capture the time development of the exponentially small transition that takes place between optimal states by means of a particular switching function. Our results confirm the physics predictions of Sir Michael Berry in the sense that the switching function for this family of Hamiltonians has the form that he argues is universal.
Publié le : 2003-09-03
Classification:  Mathematical Physics 
@article{0309012,
     author = {Hagedorn, George A. and Joye, Alain},
     title = {Time Development of Exponentially Small Non-Adiabatic Transitions},
     journal = {arXiv},
     volume = {2003},
     number = {0},
     year = {2003},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0309012}
}

Hagedorn, George A.; Joye, Alain. Time Development of Exponentially Small Non-Adiabatic Transitions. arXiv, Tome 2003 (2003) no. 0, . http://gdmltest.u-ga.fr/item/0309012/