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 Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In finite dimensions, controllability of bilinear quantum control systems canbe decided quite easily in terms of the "Lie algebra rank condition" (LARC),such that only the systems Lie algebra has to be determined from a set ofgenerators. In this paper we study how this idea can be lifted to infinitedimensions. To this end we look at control systems on an infinite dimensionalHilbert space which are given by an unbounded drift Hamiltonian and boundedcontrol Hamiltonians. The drift is assumed to have empty continuous spectrum.We use recurrence methods and the theory of Abelian von Neumann algebras todevelop a scheme, which allows us to use an approximate version of LARC, inorder to check approximate controllability of the control system in question.Its power is demonstrated by looking at some examples. We recover in particularprevious genericity results with a much easier proof. Finally several possiblegeneralizations are outlined.

Quantum control in infinite dimensions and Banach-Lie algebras: Pure point spectrum