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New Results on Smooth Controllability of Quantum Mechanical Systems | | Re-Bing Wu
; Tzyh-Jong Tarn
; Chun-Wen Li
; | | Date: |
9 May 2005 | | Subject: | quant-ph | | Abstract: | Quantum control over scattering states has potentially important applications in the future quantum technologies. However, a rigorous theoretical study is difficult due to the nonlocal nature of scattering states. This paper introduces a mathematical framework to deal with general quantum control systems that allow noncompact and infinite dimensional controllability Lie algebras, within which the generated infinite dimensional Lie groups are used to represent flows of scattering states. Then we present the concept of smooth controllability on infinite dimensional manifolds, and a criterion for approximate smooth strong controllability. This is a nontrivial extension of the existing results of controllability 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. | | Source: | arXiv, quant-ph/0505063 | | Services: | Forum | Review | PDF | Favorites | |
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