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.
Keywords
- Density Matrix
- Pair Distribution Function
- Microcanonical Ensemble
- Reduce Density Matrice
- Thermodynamic Extension
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Kita, T. (2015). Density Matrices and Two-Particle Correlations. In: Statistical Mechanics of Superconductivity. Graduate Texts in Physics. Springer, Tokyo. https://doi.org/10.1007/978-4-431-55405-9_5
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DOI: https://doi.org/10.1007/978-4-431-55405-9_5
Publisher Name: Springer, Tokyo
Print ISBN: 978-4-431-55404-2
Online ISBN: 978-4-431-55405-9
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