Anomalous structural evolution of soft particles: equibrium liquid state theory

We use the hyper-netted chain approximation of liquid state theory to analyze the evolution with density of the pair correlation function in a model of soft spheres with harmonic repulsion. As observed in recent experiments on jammed soft particles, theory predicts an 'anomalous' (nonmonotonic) evolution of the intensity of the first peak when density is increased at constant temperature. This structural anomaly is a direct consequence of particle softness, and can be explained from purely equilibrium considerations, emphasizing the generality of the phenomenon. This anomaly is also predicted to have a nontrivial, 'S-shaped', evolution with temperature, as a result of a competition between three distinct effects, which we describe in detail. Computer simulations support our predictions.