Non-hyperuniform metastable states around a disordered hyperuniform state of densely packed spheres: stochastic density functional theory at strong coupling

Abstract: Disordered and hyperuniform structures of densely packed spheres near and at jamming are characterized by vanishing of long-wavelength density fluctuations, or equivalently by long-range power-law decay of the direct correlation function (DCF). We focus on previous simulation results that exhibit degradation of hyperuniformity in jammed structures while maintaining the long-range nature of the DCF to a certain length scale. Here we demonstrate that a field-theoretic formulation of the stochastic density functional theory is relevant to explore the degradation mechanism. The strong-coupling expansion method of the stochastic density functional theory is developed to obtain the metastable chemical potential considering intermittent fluctuations in dense packings. The metastable chemical potential yields an analytical form of the metastable DCF that has a short-range cutoff inside the sphere while retaining the long-range power-law behavior. It is confirmed that the metastable DCF provides zero-wavevector limit of structure factor in quantitative agreement with the previous simulation results of degraded hyperuniformity. We can also predict the emergence of soft modes localized at the particle scale from plugging this metastable DCF into the linearized Dean-Kawasaki equation, a stochastic density functional equation.