Linking density functional and mode coupling models for supercooled liquids

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

The 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 the degradation of hyperuniformity in jammed structures while maintaining the long-range nature of the DCF to a certain length scale. Here we demonstrate that the field-theoretic formulation of stochastic density functional theory is relevant to explore the degradation mechanism. The strong-coupling expansion method of stochastic density functional theory is developed to obtain the metastable chemical potential considering the intermittent fluctuations in dense packings. The metastable chemical potential yields the 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 the zero-wavevector limit of the 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 by plugging this metastable DCF into the linearized Dean-Kawasaki equation, a stochastic density functional equation.

Localization, Disorder, and Entropy in a Coarse-Grained Model of the Amorphous Solid

We study the role of disorder in producing the metastable states in which the extent of mass localization is intermediate between that of a liquid and a crystal with long-range order. We estimate the corresponding entropy with the coarse-grained description of a many-particle system used in the classical density functional model. We demonstrate that intermediate localization of the particles results in a change of the entropy from what is obtained from a microscopic approach using for sharply localized vibrational modes following a Debye distribution. An additional contribution is included in the density of vibrational states g(ω) to account for this excess entropy. A corresponding peak in g(ω)/ω2 vs. frequency ω matches the characteristic boson peak seen in amorphous solids. In the present work, we also compare the shear modulus for the inhomogeneous solid having localized density profiles with the corresponding elastic response for the uniform liquid in the limit of high frequencies.

Dependence of the configurational entropy on amorphous structures of a hard-sphere fluid

The free energy of a hard-sphere fluid for which the average energy is trivial signifies how its entropy changes with packing. The packing η_{f} at which the free energy of the crystalline state becomes lower than that of the disordered fluid state marks the freezing point. For packing fractions η>η_{f} of the hard-sphere fluid, we use the modified weighted density functional approximation to identify metastable free energy minima intermediate between uniform fluid and crystalline states. The distribution of the sharply localized density profiles, i.e., the inhomogeneous density field ρ(x) characterizing the metastable state is primarily described by a pair function g_{s}(η/η_{0}). η_{0} is a structural parameter such that for η=η_{0} the pair function is identical to that for the Bernal random structure. The configurational entropy S_{c} of the metastable hard-sphere fluid is calculated by subtracting the corresponding vibrational entropy from the total entropy. The extrapolated S_{c} vanishes as η→η_{K} and η_{K} is in agreement with other works. The dependence of η_{K} on the structural parameter η_{0} is obtained.