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arXiv 2202.02076quant-phmath-phmath.MP
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量子中心极限定理、经典性的涌现与含时微分熵

Quantum Central Limit Theorems, Emergence of Classicality and Time-dependent Differential Entropy

Tien D. Kieu

AI总结:

本文推导了粗粒化厄米算符函数的量子中心极限定理,得到可观测量期望值的正定分布,为无穷多全同无相互作用量子组分极限下的经典性涌现提供新途径,并用于评估微分熵的含时行为。

摘要:

我们为宏观粗粒化可观测量的期望值推导出若干量子中心极限定理,这些可观测量是粗粒化厄米算符的函数。得益于厄米性约束,我们得到了可观测量期望值的正定分布。这些概率分布为在无穷多个全同且无相互作用的量子组分极限下涌现出经典行为开辟了某些途径。这与其他由环境退相干和一致性历史导致的经典性涌现机制形成对比。由此导出的概率分布还使我们能够评估某些微分熵的非平凡时间依赖性。

英文摘要:

We derive some Quantum Central Limit Theorems for expectation values of macroscopically coarse-grained observables, which are functions of coarse-grained hermitean operators. Thanks to the hermicity constraints, we obtain positive-definite distribution for the expectation values of observables. These probability distributions open some pathway for an emergence of classical behaviours in the limit of infinitely large number of identical and non-interacting quantum constituents. This is in contradistinction to other mechanisms of classicality emergence due to environmental decoherence and consistent histories. The probability distributions so derived also enable us to evaluate the nontrivial time-dependence of certain differential entropies.

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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