Pairwise and higher-order statistical correlations in excited states of quantum oscillator systems

Pairwise and higher-order statistical correlations are examined in excited states of quantum oscillator systems, in position, and in momentum space. Measures from information theory, and those based on higher-order moments of the distribution, are used to quantify the correlations. Transition points are observed in the pairwise measures as the intensity of the interaction potential is varied. The presence of these points in a particular space, is governed by the symmetry of the wave function, and the attractive or repulsive nature of the interaction potentials. Crossover points in the higher-order measures are also present, where the interaction information transits from positive to negative values as the intensity of the interaction potential increases. The interpretation is that the dominance of synergic interactions depends on the intensity of the potential. The appearance of these crossover points in a particular representation is determined by the nature of the interaction potential, and not by the symmetry of the wave function. The magnitudes of the interaction potentials at these transition and crossover points, in each space, are shown to be a consequence of a relation which establishes a functional equivalence between the wave functions in each representation. Differences in the correlation characteristics of excited and ground states are discussed.