Statistical correlations in quantum systems with explicit three-body interactions
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THE EUROPEAN PHYSICAL JOURNAL D
Regular Article
Statistical correlations in quantum systems with explicit three-body interactions Sa´ ul J. C. Salazar, Humberto G. Lagunaa , and Robin P. Sagar Departamento de Qu´ımica, Universidad Aut´ onoma Metropolitana, San Rafael Atlixco No. 186, Iztapalapa 09340, M´exico D.F., M´exico Received 5 August 2020 / Received in final form 8 October 2020 / Accepted 8 October 2020 Published online 8 December 2020 c EDP Sciences / Societ`
a Italiana di Fisica / Springer-Verlag GmbH Germany, part of Springer Nature, 2020 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.
1 Introduction The examination and analysis of probability distributions to discern and conceptualize physical behaviour has seen a rapid growth in recent years. For distributions with two or more variables, one can address the subject of the statistical correlations among these variables. If the variables represent particles, as in quantum mechanics, one can conceive of the use of these correlations to examine how strongly or how weakly the particles are interacting in the quantum system. Quantification of these correlations allows an inspection of how particle interactions influence the behaviour of a particular system [1]. Investigation of statistical correlations offers insights into how the und
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