Equilibrium Properties of Mixtures of Bosons and Fermions

TL;DR

This paper introduces Partial Quantum Nearest Neighbor Probability Density Functions (PQNNPDFs) to analyze equilibrium properties of quantum mixtures of bosons and fermions, extending classical methods to quantum systems.

Contribution

It develops a framework for quantum partial distribution functions and relates them to thermodynamic properties, including dilute and degenerate regimes.

Findings

Derived the second virial coefficient for dilute quantum mixtures.

Formulated PQNNPDFs applicable to strongly degenerate mixtures.

Connected quantum distribution functions to thermodynamic properties.

Abstract

Partial Quantum Nearest Neighbor Probability Density Functions (PQNNPDF's) are formulated for the purpose of determining the behavior of quantum mixed systems in equilibrium in a manner analogous to that provided for classical multi-component systems. Developments in partial quantum m-tuplet distribution functions, a generalization of the partial quantum radial distribution function, along with their relationship to PQNNPDF's, are briefly elucidated. The calculation of statistical thermodynamic properties of quantum mixtures is presented for arbitrary material systems. Application to the limiting case of dilute, weakly correlated quantum gas mixtures has been outlined and the second virial coefficient is derived. The case of dilute strongly degenerate mixtures is also addressed, providing an expression for the PQNNPDF applicable in this thermodynamic regime.