Correlation functions and fluctuations in the disordered fluid

From now on wc focus on situations where the fluid adsorbed by a disordered matrix is both homogeneous and isotropic after averaging over different mar trix configurations. In such a situation, the fluid s singlet density is just a constant that is, 

The expression after the first equal sign in Eq. (7.18) provides the statistical definition of the singlet density in the disordered system where 5 q — qt) — S r — Vi) for a simple fluid without internal degrees of freedom, whereas q — qi) — 6 r - Vi) d u - (jJi) for anisotropic fluid particles. The second 

Given that the singlet density is just a constant, the most important quantities characterizing the local structure within the adsorbed fluid are the two-particle correlation functions. We start by considering the pair correlation function ga q,q ) between two fluid particles or, equivalently, the corresponding total correlation function / ff q, = gg q, q ) — 1. The statis- 

Treating the double average on the right-hand side as described in Section 7.3, one finds 

The next correlation function we consider is characteristic for a quenched-annealed system in the sense that it vanishes for conventional, fully annealed fluids. This is the so-called blocked correlation function hb(q, q ) defined by 

For coiivcntiuiial fluids the outer (disorder) average of tlie first term on the right side is absent and each thermal average equals the singlet density. Thus. Ab = 0 for systems without quenched disorder. In the presence of disorder, on the other hand, the blocked correlation function is usually nonzero, because the singlet density for a particular realization, can be 

---