English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We consider a controlled Schr\"odinger equation with a dipolar and apolarizability term, used when the dipolar approximation is not valid. Thecontrol is the amplitude of the external electric field, it acts non linearlyon the state. We extend in this infinite dimensional framework previoustechniques used by Coron, Grigoriu, Lefter and Turinici for stabilization infinite dimension. We consider a highly oscillating control and prove thesemi-global weak $H^2$ stabilization of the averaged system using a Lyapunovfunction introduced by Nersesyan. Then it is proved that the solutions of theSchr\"odinger equation and of the averaged equation stay close on every finitetime horizon provided that the control is oscillating enough. Combining thesetwo results, we get approximate controllability to the ground state for thepolarizability system.

Explicit approximate controllability of the Schr\"odinger equation with a polarizability term