Higher-order statistical correlations and mutual information among particles in a quantum well

TL;DR

This paper investigates how wave function symmetry affects higher-order statistical correlations among three quantum particles in a box, revealing that symmetric states can exhibit greater multi-particle correlations than antisymmetric ones.

Contribution

It introduces the use of higher-order mutual information to quantify multi-particle correlations and compares symmetric and antisymmetric wave functions in position and momentum space.

Findings

Symmetric wave functions can be more correlated than antisymmetric ones.

Higher-order mutual information reveals correlations not captured by pairwise measures.

Results are consistent with similar behavior in three uncoupled oscillators.

Abstract

The influence of wave function symmetry on statistical correlation is studied for the case of three non-interacting spin-free quantum particles in a unidimensional box, in position and in momentum space. Higher-order statistical correlations occurring among the three particles in this quantum system is quantified via higher-order mutual information and compared to the correlation between pairs of variables in this model, and to the correlation in the two-particle system. The results for the higher-order mutual information show that there are states where the symmetric wave functions are more correlated than the antisymmetric ones with same quantum numbers. This holds in position as well as in momentum space. This behavior is opposite to that observed for the correlation between pairs of variables in this model, and the two-particle system, where the antisymmetric wave functions are in general more correlated. These results are also consistent with those observed in a system of three uncoupled oscillators. The use of higher-order mutual information as a correlation measure, is monitored and examined by considering a superposition of states or systems with two Slater determinants.