Abstract

Higher-order and pairwise statistical correlations are quantified via mutual information, in quantum systems consisting of three pairwise interacting oscillators, that are subjected to a three-body Gaussian type potential. Variational wave functions are used for these calculations. The correlation measures are calculated in both position and momentum space, to examine their dependence on the coupling strength and width of the three-body potential. Results are presented for both positive and negative three-body potentials, and attractive and repulsive two-body ones. Extremal points are observed when the pair and higher-order measures are examined as a function of the coupling strength for positive three-body potentials. This illustrates that the magnitudes of these statistical correlations can be adjusted with the strength of the three-body potential. Higher-order mutual information is positive-valued in momentum space and negative-valued in position space, in systems with attractive pair and positive three-body potentials. The interpretation is that synergistic interactions among the three particles are dominant in momentum space while the redundant (pairwise) ones prevail in position space. These behaviours are reversed in systems with repulsive pair potentials and negative three-body ones. The demeanour of the correlation measures with respect to the width of the Gaussian potential is also examined. The extremal points that are present as a function of the coupling strength, are more pronounced for broader potentials, while they disappear for narrower potentials. The positions of these extremal points move to smaller coupling strengths, as the potential narrows. Trends in the one-, two-, and three-variable Shannon entropies in these systems are also discussed.

Graphical abstract

中文翻译：

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具有明确三体相互作用的量子系统中的统计相关性

摘要

在由三个成对相互作用的振荡器组成的量子系统中，它们通过互信息来量化高阶和成对统计相关性，该量子系统受到三体高斯型电势的影响。变分波函数用于这些计算。在位置和动量空间中都计算了相关度量，以检查它们对三体势的耦合强度和宽度的依赖性。给出了正体和负体三体电位以及诱人和排斥体三体电位的结果。当对偶和高​​阶量度作为正三体电位的耦合强度的函数进行检查时，会观察到极点。这说明可以通过三体电位的强度来调整这些统计相关性的大小。在具有吸引对和正三体势的系统中，高阶互信息在动量空间中为正值，在位置空间中为负值。解释是，三个粒子之间的协同相互作用在动量空间中占主导地位，而多余的（成对）粒子在位置空间中占主导地位。在具有排斥对势和负三体势的系统中，这些行为是相反的。还检查了相关度量相对于高斯势的宽度的行为。存在的极点是耦合强度的函数，对于更宽的电势更明显，而它们消失的可能性更小。随着电位变窄，这些极值点的位置移动到较小的耦合强度。还讨论了这些系统中一变量，二变量和三变量香农熵的趋势。

图形概要