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Spatial structure of unstable normal modes in a glass-forming liquid
by Masanari Shimada, Daniele Coslovich, Hideyuki Mizuno, Atsushi Ikeda
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Daniele Coslovich · Masanari Shimada |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2009.07972v2 (pdf) |
| Date accepted: | 2020-12-15 |
| Date submitted: | 2020-11-24 05:53 |
| Submitted by: | Shimada, Masanari |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Computational |
Abstract
The phenomenology of glass-forming liquids is often described in terms of their underlying, high-dimensional potential energy surface. In particular, the statistics of stationary points sampled as a function of temperature provides useful insight into the thermodynamics and dynamics of the system. To make contact with the real space physics, however, analysis of the spatial structure of the normal modes is required. In this work, we numerically study the potential energy surface of a glass-forming ternary mixture. Starting from liquid configurations equilibrated over a broad range of temperatures using a swap Monte Carlo method, we locate the nearby stationary points and investigate the spatial architecture and the energetics of the associated unstable modes. Through this spatially-resolved analysis, originally developed to study local minima, we corroborate recent evidence that the nature of the unstable modes changes from delocalized to localized around the mode-coupling temperature. We find that the displacement amplitudes of the delocalized modes have a slowly decaying far field, whereas the localized modes consist of a core with large displacements and a rapidly decaying far field. The fractal dimension of unstable modes around the mobility edge is equal to 1, consistent with the scaling of the participation ratio. Finally, we find that around and below the mode-coupling temperature the unstable modes are localized around structural defects, characterized by a disordered local structure markedly different from the liquid's locally favored structure. These defects are similar to those associated to quasi-localized vibrations in local minima and are good candidates to predict the emergence of localized excitations at low temperature.
Author comments upon resubmission
List of changes
1. Shorten the introduction slightly (referee 2).
2. Add a note in Sec. IIA saying that a few crystallized samples were removed from the analysis
3. Add the definition of the mode-coupling temperature (referee 3).
4. Add a more detailed description of convergence issues of the EF optimizations in Sec. IIA (referee 1).
5. Add the definition of the ceiling function in Sec. IIB3 (referee 2).
6. Extend the explanation of the energy profile in Sec. IIB4 (referee 2).
7. Change the dashed lines in Fig. 1 to the solid lines (referee 1).
8. Revise the definition and discussion of the mobility edge in Sec. IIIA based on Ref. [26] (referee 2 and 3).
9. Add the fraction of delocalized modes in Tab. I (referee 2).
10. Add an estimation of the system size needed to observe the asymptotic scaling in Fig. 3, see the footnote on page 7 (referee 3).
11. Weaken the emphasis on the difference between unstable delocalized modes and the QLVs in Fig. 4 (referee 2).
12. Weaken the emphasis on the difference between Voronoi signatures (referee 2).
13. Add the calculation of the Tong-Tanaka Theta order parameter to characterize the local structure of the core particles (referee 2)
Published as SciPost Phys. 10, 001 (2021)
Reports on this Submission
Report #2 by Anonymous (Referee 1) on 2020-11-24 (Invited Report)
- Cite as: Anonymous, Report on arXiv:2009.07972v2, delivered 2020-11-24, doi: 10.21468/SciPost.Report.2229
Strengths
A thorough study on a topic not yet addressed.
Weaknesses
No major weakness in particular.
Report
The authors have done excellent work in addressing all referees' concerns and in producing a better-revised version of the manuscript with a new analysis of the structure at the unstable cores. I recommend the publication of the manuscript.
Report #1 by Anonymous (Referee 2) on 2020-11-24 (Invited Report)
- Cite as: Anonymous, Report on arXiv:2009.07972v2, delivered 2020-11-24, doi: 10.21468/SciPost.Report.2226
Strengths
- Clear
- Insightful
- Detailed
Weaknesses
No major weaknesses were identified.
Report
The resubmission addresses all the points raised in the first round of peer-reviewing. It also provides further analysis and insight on the local structure of the saddles and of the unstable cores. I do recommend publication in the current form.