title: Force distribution affects vibrational properties in hard-sphere glasses.
abstract: We theoretically and numerically study the elastic properties of hard-sphere glasses and provide a real-space description of their mechanical stability. In contrast to repulsive particles at zero temperature, we argue that the presence of certain pairs of particles interacting with a small force f soften elastic properties. This softening affects the exponents characterizing elasticity at high pressure, leading to experimentally testable predictions. Denoting P(f) ~ f(θ(e)), the force distribution of such pairs and ϕ(c) the packing fraction at which pressure diverges, we predict that (i) the density of states has a low-frequency peak at a scale ω*, rising up to it as D(ω) ~ ω(2+a), and decaying above ω* as D(ω) ~ ω(-a) where a = (1 - θ(e))/(3 + θ(e)) and ω is the frequency, (ii) shear modulus and mean-squared displacement are inversely proportional with ⟨δR²⟩ ~ 1/μ ~ (ϕ(c) - ϕ)(κ), where κ = 2 - 2/(3 + θ(e)), and (iii) continuum elasticity breaks down on a scale ℓ(c) ~ 1/√(δz) ~ (ϕ(c) - ϕ)(-b), where b = (1 + θ(e))/(6 + 2θ(e)) and δz = z - 2d, where z is the coordination and d the spatial dimension. We numerically test (i) and provide data supporting that θ(e) ≈ 0.41 in our bidisperse system, independently of system preparation in two and three dimensions, leading to κ ≈ 1.41, a ≈ 0.17, and b ≈ 0.21. Our results for the mean-square displacement are consistent with a recent exact replica computation for d = ∞, whereas some observations differ, as rationalized by the present approach.
authors.affiliation: Center for Soft Matter Research, New York University, New York, NY 10003; ed87@nyu.edu.
authors.forename: Eric
authors.initials: E
authors.lastname: DeGiuli
authors.affiliation: Center for Soft Matter Research, New York University, New York, NY 10003; Institute for Theoretical Physics, Institute of Physics, University of Amsterdam, 94485 Amsterdam, The Netherlands; and.
authors.forename: Edan
authors.initials: E
authors.lastname: Lerner
authors.affiliation: Instituto de Fisica da Universidade Federal do Rio Grande do Sul, C.P. 15051 Porto Alegre, RS, Brazil.
authors.forename: Carolina
authors.initials: C
authors.lastname: Brito
authors.affiliation: Center for Soft Matter Research, New York University, New York, NY 10003;
authors.forename: Matthieu
authors.initials: M
authors.lastname: Wyart
keywords: boson peak; colloids; glass transition; jamming; marginal stability