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Liquid is More Rigid than Solid in a High-Frequency Region

We compare rigidity of materials in two phases, liquid and solid phases. As a measure of the rigidity, we employ the one characterizing how firmly the material is fixed by low density of pinning centers, such as impurities and rough surfaces of walls, against a weak force. Although a solid is more rigid than a liquid against a low-frequency force, we find that against a high-frequency force the liquid becomes more rigid than the solid of the same material. Since this result is derived from universal properties of a response function, it is valid for wide classes of materials, including quantum and classical systems and crystalline and amorphous solids. An instructive example is studied using nonequilibrium molecular dynamics simulations. We find that the frequency region in which a solid is more flexible than a liquid is not purely determined by intrinsic properties of the solid. It depends also on extrinsic factors such as the density of pinning centers.