Journal of Statistical Physics, Vol. 45, Nos. 5/6, 1986, p. 815-841.
We study the poor decay of correlations for equilibrium states of inhomogeneous fluids and solids, in the regimes of both classical and quantum statistical mechanics. Our main observation is the usefulness of the statistical mechanical expression of the stress tensor and its long-range correlations with the particle density. From this we are able to infer a very slow decay of correlations for the various molecular distribution functions under discussion. The derived results are of relevance both for completely inhomogeneous systems such as quasicrystals or granular structures and for the slightly more regular cases of, e.g., phase separating layers in fluids and solids, ideal crystals, etc. As one of the byproducts we prove the nonexistence of plane quantum interfaces in two dimensions (thus extending earlier results of Requardt to the quantum regime). The results hold for arbitrary potentials of not too long range.