CHAIN RELATIONS OF REDUCED DISTRIBUTION-FUNCTIONS AND THEIR ASSOCIATED CORRELATION-FUNCTIONS

For a closed system, the integration (trace in the quantum case) over one particle of a reduced distribution function is related to the redu ced distribution function of one lower order, The particular details o f this ''chain'' relation depend sensitively on the detailed manner in which the reduced distribution functions are defined, specifically th eir normalization. Correlation functions are defined in terms of reduc ed distribution functions, which fixes the normalization of the correl ation functions and, provided they exist, their associated chain relat ions. Chain relations for the correlation functions are shown to exist for normalizations of generic type but not for normalizations of spec ific type. The normalization requirement is shown, in general, to prev ent the direct association of correlation functions with physical clus ters, which is commonly assumed in the literature, These relations are illustrated for an ideal gas of monomers and dimers. The effect of ta king the thermodynamic limit on the chain relations for this system is discussed. This illustrates how the thermodynamic limit generally des troys the chain relations. (C) 1998 American Institute of Physics.