Generalizing our recent work on relativistic generalizations of the quantum theory of atoms in molecules, we present the general setting under which the principle of stationary action for a region leads to open quantum subsystems. The approach presented here is general and works for any Hamiltonian, and when a reasonable Lagrangian is selected, it often leads to the integral of the Laplacian of the electron density on the region vanishing as a necessary condition for the zero‐flux surface. Alternatively, with this method, one can design a Lagrangian that leads to a surface of interest (though this Lagrangian may not be, and indeed probably will not be, “reasonable”). For any reasonable Lagrangian for the electronic wave function and any two‐component method (related by integration by parts to the Hamiltonian) considered, the Bader definition of an atom is recaptured. © 2018 Wiley Periodicals, Inc.

中文翻译：

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零通量条件的一般设置：给出海森堡运动方程的拉格朗日和零通量条件

概括我们最近在分子中原子的量子理论的相对论概括方面的工作，我们提出了一般设置，在该设置下，区域的静止作用原理导致开放量子子系统。The approach presented here is general and works for any Hamiltonian, and when a reasonable Lagrangian is selected, it often leads to the integral of the Laplacian of the electron density on the region vanishing as a necessary condition for the zero‐flux surface. 或者，使用这种方法，人们可以设计一个拉格朗日函数来导致感兴趣的表面（尽管这个拉格朗日函数可能不是，实际上可能不会，“合理”）。对于任何合理的电子波函数拉格朗日和任何双分量方法（通过部分积分与哈密顿量相关），重新定义原子的 Bader 定义。© 2018 Wiley Periodicals, Inc.