An Optimal Control Perspective on Classical and Quantum Physical Systems

IF 2.2 3区 综合性期刊 Q2 MULTIDISCIPLINARY SCIENCES Symmetry-Basel Pub Date : 2023-11-08 DOI:10.3390/sym15112033
Mauricio Contreras G., Marcelo Villena
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Abstract

This paper analyzes 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 a closed-loop feedback problem can describe it. Secondly, for a quantum physical system, if one realizes that the Heisenberg commutation relations themselves can be considered constraints in a non-commutative space, then the momentum must depend on the position of any generic wave function. That implies the existence of a closed-loop strategy for the quantum case. Thus, closed-loop feedback is a natural phenomenon in the physical world. By way of completeness, we briefly review control theory and the classical mechanics of constrained systems and analyze some examples at the classical and quantum levels.
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经典和量子物理系统的最优控制观点
本文从最优控制的角度分析了经典物理系统和量子物理系统。具体而言,我们探讨了它们的相关动力学是否可以对应于控制问题的开环或闭环反馈演化。首先,对于经典状态,从正则变换理论的角度来看,我们发现闭环反馈问题可以描述它。其次,对于量子物理系统,如果人们意识到海森堡对易关系本身可以被认为是非对易空间中的约束,那么动量必须依赖于任何一般波函数的位置。这意味着在量子情况下存在闭环策略。因此,闭环反馈是物理世界中的一种自然现象。为了完备性,我们简要地回顾了约束系统的控制理论和经典力学,并在经典和量子水平上分析了一些例子。
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来源期刊
Symmetry-Basel
Symmetry-Basel MULTIDISCIPLINARY SCIENCES-
CiteScore
5.40
自引率
11.10%
发文量
2276
审稿时长
14.88 days
期刊介绍: Symmetry (ISSN 2073-8994), an international and interdisciplinary scientific journal, publishes reviews, regular research papers and short notes. Our aim is to encourage scientists to publish their experimental and theoretical research in as much detail as possible. There is no restriction on the length of the papers. Full experimental and/or methodical details must be provided, so that results can be reproduced.
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