论文标题
对经典和量子物理系统的最佳控制观点
An Optimal Control Perspective on Classical and Quantum Physical Systems
论文作者
论文摘要
在本文中，我们从最佳控制角度分析了经典和量子物理系统。具体来说，我们探索它们相关的动态是否可以对应于控制问题的开放或闭环反馈演变。首先，对于经典制度，当它从规范转换理论方面进行查看时，我们发现它可以通过闭环反馈问题来描述。其次，对于量子物理系统，如果人们意识到Heisenberg的换向关系本身可以被视为在非交通空间中的约束，那么动量必须取决于任何通用波浪函数的位置。这意味着存在量子案例的闭环策略。因此，闭环反馈是物理世界中的自然现象。为了展示，我们对控制理论进行了简短的审查，并分析了经典和量子水平的一些熟悉的例子。
In this paper, we analyze classical and quantum physical systems from an optimal control perspective. Specifically, we explore whether their associated dynamics can correspond to an open or closed-loop feedback evolution of a control problem. Firstly, for the classical regime, when it is viewed in terms of the theory of canonical transformations, we find that it can be described by a closed-loop feedback problem. Secondly, for a quantum physical system, if one realizes that the Heisenberg commutation relations themselves can be thought of as constraints in a non-commutative space, then the momentum must be dependent on the position for any generic wave function. This implies the existence of a closed-loop strategy for the quantum case. Thus, closed-loop feedback is a natural phenomenon in the physical world. For the sake of exposition, we give a short review of control theory, and some familiar examples at the classical and quantum levels are analyzed.
