Quantum structure of normal-liquid and supercriticalH4e

Abstract

We study the temperature dependence of various spatial correlation functions of normal fluid and liquid $^{4}\text{H}\text{e}$ along an isochoric line of particle number density $\ensuremath{\varrho}=0.02185\text{ }{\text{\AA{}}}^{\ensuremath{-}3}$. The formal and numerical investigation employs correlated density-matrix theory as currently developed. The formalism permits a clear analysis of particle exchange (statistical) effects and so-called direct-direct quantum effects that appear only in a many-body system of interacting particles. At supercritical temperatures $T\ensuremath{\ge}12\text{ }\text{K}$ the helium fluid can be characterized as a perfect quantum Boltzmann system. In such a fluid, quantum statistical correlations are absent and the particle exchange follows classical Boltzmann statistics despite direct-direct quantum effects being present. At temperatures below 12 K, statistical quantum correlations begin to appear and are largest at the Bose-Einstein transition temperature ${T}_{\text{BE}}=2.17\text{ }\text{K}$. However, these correlations are considerably smaller than the statistical exchange correlations existing in a free Bose gas of bosons with helium mass. We present analytical and numerical results on the radial distribution function, the exchange correlation function, the phase-phase correlation function, the one-body reduced density matrix, and gross thermal quantities such as specific heat and total exchange energy. The role of particle exchange in determining their quantum properties is analyzed and discussed in detail.