On the Classical Limit of Freely Falling Quantum Particles, Quantum Corrections and the Emergence of the Equivalence Principle

IF 2.5 4区 物理与天体物理 Q2 ASTRONOMY & ASTROPHYSICS
Universe Pub Date : 2024-09-02 DOI:10.3390/universe10090351
Juan A. Cañas, J. Bernal, A. Martín-Ruiz
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引用次数: 0

Abstract

Quantum and classical mechanics are fundamentally different theories, but the correspondence principle states that quantum particles behave classically in the appropriate limit. For high-energy periodic quantum systems, the emergence of the classical description should be understood in a distributional sense, i.e., the quantum probability density approaches the classical distribution when the former is coarse-grained. Following a simple reformulation of this limit in the Fourier space, in this paper, we investigate the macroscopic behavior of freely falling quantum particles. To illustrate how the method works and to fix some ideas, we first successfully apply it to the case of a particle in a box. Next, we show that, for a particle bouncing under the gravity field, in the limit of a high quantum number, the leading term of the quantum distribution corresponds to the exact classical distribution plus sub-leading corrections, which we interpret as quantum corrections at the macroscopic level.
论自由落体量子粒子的经典极限、量子修正和等效原理的出现
量子力学和经典力学从根本上说是不同的理论,但对应原理指出,量子粒子在适当的限度内具有经典行为。对于高能周期量子系统,经典描述的出现应从分布的角度来理解,即当前者的分布粗粒度时,量子概率密度接近经典分布。本文通过在傅立叶空间对这一极限的简单重述,研究了自由下落量子粒子的宏观行为。为了说明该方法的工作原理并固定一些想法,我们首先成功地将其应用于一个盒子中的粒子的情况。接下来,我们证明,对于在引力场下反弹的粒子,在高量子数的极限下,量子分布的前导项对应于精确的经典分布加上次前导修正,我们将其解释为宏观层面的量子修正。
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来源期刊
Universe
Universe Physics and Astronomy-General Physics and Astronomy
CiteScore
4.30
自引率
17.20%
发文量
562
审稿时长
24.38 days
期刊介绍: Universe (ISSN 2218-1997) is an international peer-reviewed open access journal focused on fundamental principles in physics. It publishes reviews, research papers, communications, conference reports and short notes. Our aim is to encourage scientists to publish their research results in as much detail as possible. There is no restriction on the length of the papers.
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