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Leggett's bound for amorphous solids

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FIG. 1: Leggett upper bound for ρ s /ρ, for a Gaussian profile of width A 1 / 2 around an amorphous jammed configuration and in a FCC lattice, as a function of the adimensional  pa-rameter ℓ = ρ 1 / 3 A 1 / 2 (the Lindemann ratio).
TABLE I: Leggett’s bound for He 4 in the HCP crystal state [29] and glassy state. Quantum Monte Carlo results for the glass are also reported [6].
FIG. 3: Evolution of the density profile after a quench from high to low temperature for a quantum Helium 4 system, using Path Integral Monte Carlo
FIG. 4: Result for ρ s /ρ as a function of ℓ = ρ 1 / 3 A 1 / 2 , where R~ i are the center of the spheres in an amorphous jammed configuration of N spheres with periodic boundary conditions.
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