2005/05/31 by Re-Bing Wu, Tzyh‐Jong Tarn, Tzyh-Jong Tarn +2 · 2 citations
Mathematics · Physics and Astronomy · #Laser-Matter Interactions and Applications #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics #quant-ph
paper · pdf · doi:10.1103/physreva.73.012719
arxiv created 2005/12/12 · openalex publication_date 2006/01/31 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Manipulation of infinite-dimensional quantum systems is important to controlling complex quantum dynamics with many practical physical and chemical backgrounds. In this paper, a general investigation is casted to the controllability problem of quantum systems evolving on infinite-dimensional manifolds. Recognizing that such problems are related with infinite-dimensional controllability algebras, we introduce an algebraic mathematical framework to describe quantum control systems possessing such controllability algebras. Then we present the concept of smooth controllability on infinite-dimensional manifolds, and draw the main result on approximate strong smooth controllability. This is a nontrivial extension of the existing controllability results based on the analysis over finite-dimensional vector spaces to analysis over infinite-dimensional manifolds. It also opens up many interesting problems for future studies.