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任意形状双势垒的共振隧穿:最小空间尺度的存在的检验

Penetration of Arbitrary Double Potential Barriers with Probability Unity: Implications for Testing the Existence of a Minimum Length

摘要:我们人类生活的三维空间(实空间)是连续的吗?换句话说,实空间是无限可分的么?在宏观世界里,答案无疑是肯定的,因为日常生活的经验,如看到的流水,奔跑的动物,空中的飞鸟,以及自由下落的物体,无一例外的给予人们连续轨迹的印象。在经典力学中,用连续的坐标来描写运动物体被认为是理所当然的。 在量子世界里面,情况会发生戏剧性的变化。例如,当一个粒子的运动受到限制的时候,它的稳定态的能量只能取一些的离散值。一些尝试统一量子力学和引力的现代理论预测了一个最小长度的存在,通常取为普朗克尺度,这个长度大约是1.610-35米。然而,这个长度的实验检验是极具挑战性的,因为它远小于LIGO能测量的最小长度(大约是10-19米)。 在本项工作中,作者研究了任意形状的双势垒体系的量子隧穿现象并证明了一个定理。这个定理表明,如果两个势垒之间的间距可以连续变化,即实空间是连续的,则只要适当地调节势垒间距,入射粒子就可以完全穿透双势垒体系。这种现象通常被称为共振隧穿。反之,如果实空间是不连续的,即存在一个非零的最小尺度,则当势垒的尺寸超过某个上限值的时候,共振隧穿现象就不再发生。这个工作揭示了量子隧穿现象和量子引力理论中最小尺度的深刻联系,开辟了检验最小尺度的存在性的新途径。

英文摘要:Quantum tunneling across double potential barriers is studied. With the assumption that the real space is a continuum, it is rigorously proved that large barriers of arbitrary shapes can be penetrated by low-energy particles with a probability of unity, i.e., realization of resonant tunneling (RT), by simply tuning the inter-barrier spacing. The results are demonstrated by tunneling of electrons and protons, in which resonant and sequential tunneling are distinguished. The critical dependence of tunneling probabilities on the barrier positions not only demonstrates the crucial role of phase factors, but also points to the possibility of ultrahigh accuracy measurements near resonance. By contrast, the existence of a nonzero minimum length puts upper bounds on the barrier size and particle mass, beyond which effective RT ceases. A scheme is suggested for dealing with the practical difficulties arising from the delocalization of particle position due to the uncertainty principle. This work opens a possible avenue for experimental tests of the existence of a minimum length based on atomic systems.

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[V2] 2022-07-29 18:37:27 chinaXiv:202206.00123V2 下载全文
[V1] 2022-06-09 10:08:04 chinaXiv:202206.00123v1 查看此版本 下载全文
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