Adiabatic control of the Schrödinger equation via conical intersections of the eigenvalues

Abstract : In this paper, we present a constructive method to control the bilinear Schrödinger equation via two controls. The method is based on adiabatic techniques and works if the spectrum of the Hamiltonian admits eigenvalue intersections, and if the latter are conical (as it happens generically). In this framework, we are able to spread on several levels connected by conical intersections a state initially concentrated in a single energy level. We provide sharp estimates on the dependence of the error with respect to the controllability time. Moreover, we identify some special curves in the space of controls that improve the precision of the adiabatic approximation, when passing through conical intersections, with respect to classical adiabatic theory.
Document type :
Journal articles
Complete list of metadatas

Cited literature [30 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-00565773
Contributor : Francesca Carlotta Chittaro <>
Submitted on : Tuesday, February 15, 2011 - 8:56:39 AM
Last modification on : Tuesday, April 2, 2019 - 2:03:40 AM
Long-term archiving on : Monday, May 16, 2011 - 2:50:58 AM

Files

adiabatic-control.pdf
Files produced by the author(s)

Identifiers

Citation

Ugo Boscain, Francesca Chittaro, Paolo Mason, Mario Sigalotti. Adiabatic control of the Schrödinger equation via conical intersections of the eigenvalues. IEEE Transactions on Automatic Control, Institute of Electrical and Electronics Engineers, 2012, 57 (8), pp.1970-1983. ⟨10.1109/TAC.2012.2195862⟩. ⟨hal-00565773⟩

Share

Metrics

Record views

1324

Files downloads

474