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arXiv 2201.05183gr-qchep-thquant-ph
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一种利用遵循一般分布的波包探测普朗克尺度的新机制

A novel mechanism for probing the Planck scale with wavepackets following general distributions

Saurya Das, Sujoy K. Modak

备注：
v2, 27 pages, 6 improved figures, matches published version in European Physical Journal Plus
发表信息：
Eur. Phys. J. Plus (2023) 138: 366
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AI总结：

本文将GUP对波包倍增时间的修正研究从高斯分布推广到任意分布，利用量子-统计对偶性构建形式体系，并通过数值研究发现TPPF152有机波包在广义正态分布下可扫描GUP参数空间至普朗克值百倍。

摘要：

最近的研究还表明，GUP（广义不确定性原理）预言了自由运动的高斯原子和分子波包的“倍增时间”存在潜在可测量的修正，这需要三个参数的有利组合，例如运动波包的质量、初始宽度和平均速度。然而，众所周知，这类波包可以具有各种形状，对应多种不同的分布。在本文中，我们将早期工作推广到任意分布，从而能够容纳任何形状的波包。在数学上，我们通过利用量子力学与统计力学之间的对偶性来构建这一形式体系，借此（量子力学的）动量算符期望值可以用对偶统计描述的特征函数的导数来表示。基于这一结果，我们进一步对若干物理分布进行了数值研究。我们发现，遵循参数κ=0.5的广义正态分布的大有机（TPPF152）波包提供了最佳情形之一，能够利用当前技术有效扫描整个GUP参数空间。尽管我们并未声称最小长度必须接近或等于普朗克值，但我们设法改进了先前的研究，将最小长度特征信号的扫描范围推进到普朗克值的一百倍。

英文摘要：

It was also shown recently that GUP predicts potentially measurable corrections to the `doubling time' of freely moving Gaussian atomic and molecular wavepackets with a favorable combination of three parameters, {\it e.g.} mass, initial width and mean velocity of a travelling wavepacket. However, it is well known that such wavepackets can come with various shapes which correspond to variety of distributions. In this article, we generalize our earlier work for an {\it arbitrary distribution} and thereby accommodate any shape of the wavepacket. Mathematically, we build this formalism by exploiting a duality between quantum and statistical mechanics, by which (quantum mechanical) expectation values of the momentum operator can be expressed in terms of the derivatives of the characteristic functions of the dual statistical description. Equipped with this result, we go one step further and numerically study a few physical distributions. We find that large organic (TPPF152) wavepacket following the generalized normal distribution with parameter $κ=0.5$ offers one of the best-case scenarios, effectively scanning the whole GUP parameter space with current technologies. Although we do not say that the minimal length has to be near or at the Planck value, we mange improving our previous studies to scan the minimal length signatures down to hundred times the Planck value.

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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