In finite dimensions, controllability of bilinear quantum control systems can be 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 of generators. In this paper we study how this idea can be lifted to infinite dimensions. To this end we look at control systems on an infinite dimensional Hilbert space which are given by an unbounded drift Hamiltonian H_0 and bounded control Hamiltonians H_1,..., H_N. The drift H_0 is assumed to have empty continuous spectrum. We use recurrence methods and the theory of Abelian von Neumann algebras to develop a scheme, which allows us to use an approximate version of LARC, in order to check approximate controllability of the control sysPtem in question.
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机译：在有限尺寸中，就“Lie代数等级条件”（LARC）而言，可以很容易地决定双线性量子控制系统的可控性，使得仅从一组发电机确定系统LIE代数。在本文中，我们研究了如何将这个想法升到无限尺寸。为此，我们在无限维的Hilbert空间上看控制系统，该系统由无限的漂移哈密顿H_0给出，并有界控制Hamiltonians H_1，...，H_N。假设漂移H_0具有空的连续频谱。我们使用复制方法和abelian von Neumann代数的理论来开发一个方案，它允许我们使用近似的LARC版本，以检查所讨论的控制SYSPTEM的近似可控性。
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