MARKOFFIAN SPATIAL PROCESSES AND SPATIAL CORRELATIONS BETWEEN LOCAL STRUCTURES

Abstract
Local structures at different points in space can be compared when they are defined in terms of a common set of parameters (local structure parameters) which may vary randomly from one point in space to another. An example of such parameters is provided by the local quasi-lattice, randomly translated and rotated in space. The spatial correlations between local quasi-lattices are derived from a spatial Fokker-Planck type theory. From these correlations one can derive the radial distribution as well as the bond orientational correlations in the liquid and non-crystalline solid. The theory is extended to include different types of local symmetries (quasi-lattices) and the spatial transition probability between them.