This paper presents sufficient and necessary conditions for the propagator controllability of a class of infinite-dimensional quantum systems with SU(1, 1) dynamical symmetry through the isomorphic mapping to the non-unitary representation of SU(1, 1). We prove that the elliptic condition of the total Hamiltonian is both necessary and sufficient for the controllability and strong controllability. The obtained results can be also extended to control systems with SO(2, 1) dynamical symmetry.

中文翻译：

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SU（1，1）动态对称的量子系统的可控性

本文提出了一类无限维量子系统中的与传播控制性充分必要条件SU（1，1）动力学对称性通过同构映射到的非统一表示SU（1，1）。我们证明了总哈密顿量的椭圆条件对于可控性和强可控性都是必要和充分的。获得的结果还可以扩展到具有SO（2，1）动态对称性的控制系统。