Statistical correlations in quantum systems with explicit three-body interactions

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.