Abstract
Static and dynamic properties in dense many-body systems are considered from a unified point of view that emphasizes geometric features of the potential energy function c1 for interparticle interactions. Steepest descent mapping on the c1 hypersurface generates a natural division of the multidimensional configuration space into basins whose boundaries contain the fundamental transition states for the system as a whole. The resulting statistical representation (a) identifies an inherent structure for the liquid state, (b) leads to a simple description of phase transitions, (c) offers a natural formalism for supercooled liquids, and (d) provides an analysis of relaxation phenomena in glasses. Classical mechanics is used throughout the development.
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