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Physical significance of high‑frequency anti‑correlations between vDOS and defect count

Determine the physical significance and origin of the strong anti-correlations observed at large frequencies between the vibrational density of states D(ω) and the total number of topological defects N_d(ω), computed from the eigenvector field of normal modes of the mass‑rescaled Hessian in the experimental two‑dimensional dipolar colloidal glass; in particular, explain the anti‑correlation seen for ω ∈ [250, 340], where D(ω) decreases while N_d(ω) increases.

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Background

The paper measures the vibrational density of states D(ω) from the eigenvalues of a mass‑rescaled Hessian built from a 2D dipolar colloidal glass and identifies topological defects by integer winding numbers in the eigenvector fields. Across most of the spectrum, D(ω) and the total number of defects N_d(ω) are strongly and positively correlated, with both quantities scaling linearly at low frequencies in the Debye regime.

However, the authors report a pronounced anti‑correlation at higher frequencies, notably in the range ω ∈ [250, 340], where D(ω) decreases while N_d(ω) continues to increase. They explicitly state that they lack a concrete understanding of the physical significance of these high‑frequency anti‑correlations, motivating a focused theoretical investigation into their origin and implications for the structure and dynamics of the system.

References

Particularly noteworthy is the presence of such anti-correlation within the frequency range ω ∈ [250, 340], prompting further theoretical investigation to unravel its origin and its consequential impact on the system's structure and dynamics. At this moment, we do not have a concrete understanding of the physical significance of these anti-correlations appearing at large frequencies, above the Debye regime where both N_d(ω) and D(ω) scale like ω (and nicely correlate).

— Experimental identification of topological defects in 2D colloidal glass (2405.06494 - Vaibhav et al., 10 May 2024) in Section Topological defects, discussion of Fig. 4a–b (Correlation between vibrational density of states and number of topological defects)