Laplace变换势延迟响应函数的可逆性：在单体约化密度矩阵泛函理论中的应用
Invertibility of retarded response functions for Laplace transformable potentials: application to one-body reduced density matrix functional theory
摘要：
本文给出了任意响应函数可逆性的一个定理，条件是：响应函数的时间依赖性是Laplace可变换的，初始态是基态，尽管它可能是简并的。这一定理为含时线性响应体系中的所有密度泛函理论提供了严格的基础。特别是对于含时单体约化密度矩阵（1RDM）泛函理论，这是向前迈出的重要一步，因为目前缺乏坚实的基础。该定理对于非简并情形下的静态响应函数同样有效，因此可以用来刻画相应的类密度泛函理论的基态版本中势的唯一性。这样一种对基态1RDM泛函理论中非定域势唯一性的分类，几十年来一直缺乏。借助于本文提出的可逆性定理，首次对1RDM泛函理论中非定域势的非唯一性给出了一个完整的分类。
英文摘要：
A theorem for the invertibility of arbitrary response functions is presented under the following conditions: the time-dependence of the potentials should be Laplace transformable and the initial state should be a ground state, though it might be degenerate. This theorem provides a rigorous foundation for all density-functional-like theories in the time-dependent linear response regime. Especially for time-dependent one-body reduced density matrix (1RDM) functional theory this is an important step forward, since a solid foundation has currently been lacking. The theorem is equally valid for static response functions in the non-degenerate case, so can be used to characterize the uniqueness of the potential in the ground state version of the corresponding density-functional-like theory. Such a classification of the uniqueness of the non-local potential in ground state 1RDM functional theory has been lacking for decades. With the aid of presented invertibility theorem presented here, a complete classification of the non-uniqueness of the non-local potential in 1RDM functional theory can be given for the first time.
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