Density Matrices and Two-Particle Correlations

Abstract

In this chapter, we first introduce two new concepts named density matrix and reduced density matrices as (5.1) and (5.3). The reduced density matrices are closely connected with the n-particle correlations in equilibrium (n = 1, 2, ⋯ ). Next, we give a proof of the Bloch–De Dominicis theorem, i.e., a thermodynamic extension of Wick’s theorem, which enables us to express the n-particle correlations of ideal gases in terms of one-particle correlations as (5.11). Finally, the theorem is applied to obtain the two-particle correlations of homogeneous ideal Bose and Fermi gases in three dimensions. The results are summarized in Fig. 5.1 below. It clearly shows that there exists a special quantum-mechanical correlation between each pair of identical particles due to the permutation symmetry, which is completely different in nature between Bose and Fermi gases.