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arXiv 2201.10344quant-ph
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经典与量子理论中的测量

The measurement in classical and quantum theory

Alexey A. Kryukov

AI总结:

本文在经典与量子力学的几何关系背景下扩展了BGS猜想,提出经典对应物执行随机游走的系统Hamiltonian可由Gaussian幺正系综独立随机矩阵建模,从而揭示了经典与量子观测过程的关系、观测不可逆性及微观与宏观边界。

摘要:

Bohigas-Giannoni-Schmit (BGS) 猜想指出,经典混沌系统的微观类似物的 Hamiltonian 可以用来自 Gaussian 系综的随机矩阵来建模。本文在经典与量子力学之间近期发现的几何关系的背景下考虑了该猜想。受 BGS 启发,我们猜想其经典对应物执行随机游走的系统的 Hamiltonian 可以用来自 Gaussian 幺正系综的一族独立随机矩阵来建模。通过接受这一猜想,我们找到了经典与量子物理中观测过程之间的关系,推导了观测的不可逆性,并描述了微观与宏观世界之间的边界。

英文摘要:

The Bohigas-Giannoni-Schmit (BGS) conjecture states that the Hamiltonian of a microscopic analogue of a classical chaotic system can be modeled by a random matrix from a Gaussian ensemble. Here, this conjecture is considered in the context of a recently discovered geometric relationship between classical and quantum mechanics. Motivated by BGS, we conjecture that the Hamiltonian of a system whose classical counterpart performs a random walk can be modeled by a family of independent random matrices from the Gaussian unitary ensemble. By accepting this conjecture, we find a relationship between the process of observation in classical and quantum physics, derive irreversibility of observation and describe the boundary between the micro and macro worlds.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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