Abstract
The work aims to show that small system sizes in numerical simulations turns out to be useful for investigating the Debye spectrum in glasses.
Highlights
The low-frequency portion of the vibrational density of states (DOS) D(ω) in topologically disordered systems is dominated by Goldstone modes whose DOS is proportional to ωd−1, where d is the spatial dimension
We investigate the low-frequency spectrum in a three-dimensional model of structural glass focusing on small system sizes, and using different observables, i.e., the density of states D(ω), the cumulative of the density of states F (ω), and the dynamical structure factor S(q, ω) in the harmonic approximation
Considering small system sizes, in the present paper, we show that different observables such as the DOS D(ω), the cumulative F (ω), and the dynamical structure factor S(q, ω) suggest that the spectrum below the lowest resonant mode still follows Debye’s law in homogenous glasses, i.e., glassy configurations obtained after an instantaneous quench from T = ∞
Summary
The low-frequency portion of the vibrational density of states (DOS) D(ω) in topologically disordered systems is dominated by Goldstone modes (spatially extended quasiphonon modes) whose DOS is proportional to ωd−1, where d is the spatial dimension. We have observed a continuous transition of the DOS from ω2 (high parental temperature, no heterogeneity) toward ω4 (low parental temperature, large heterogeneity) In all these studies we used “small systems,” i.e., up to N = 203, where—as we found—many excitations have frequencies below the lowest resonant mode. Considering small system sizes, in the present paper, we show that different observables such as the DOS D(ω), the cumulative F (ω), and the dynamical structure factor S(q, ω) suggest that the spectrum below the lowest resonant mode still follows Debye’s law in homogenous glasses, i.e., glassy configurations obtained after an instantaneous quench from T = ∞. Configurations taken at parental temperatures close to the dynamic transition, i.e., where dynamical heterogeneities proliferate, maintain almost untouched the resonant mode They lose extended modes at lower frequencies and the only lowenergy excitations below ω0, i.e., the lowest resonant modes, are soft-localized modes
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