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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 non-trivial, `${\cal S}$-shaped', evolution with temperature, as a result of a competition between three distinct effects, which we describe in detail. Computer simulations support our predictions.