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Nonlinear modes disentangle glassy and Goldstone modes in structural glasses

by Luka Gartner, Edan Lerner

Submission summary

As Contributors: Edan Lerner
Arxiv Link: (pdf)
Date accepted: 2016-12-31
Date submitted: 2016-12-21 01:00
Submitted by: Lerner, Edan
Submitted to: SciPost Physics
Academic field: Physics
  • Condensed Matter Physics - Theory
  • Statistical and Soft Matter Physics
Approaches: Theoretical, Computational


One outstanding problem in the physics of glassy solids is understanding the statistics and properties of the low-energy excitations that stem from the disorder that characterizes these systems' microstructure. In this work we introduce a family of algebraic equations whose solutions represent collective displacement directions (modes) in the multi-dimensional configuration space of a structural glass. We explain why solutions of the algebraic equations, coined nonlinear glassy modes, are quasi-localized low-energy excitations. We present an iterative method to solve the algebraic equations, and use it to study the energetic and structural properties of a selected subset of their solutions constructed by starting from a normal mode analysis of the potential energy of a model glass. Our key result is that the structure and energies associated with harmonic glassy vibrational modes and their nonlinear counterparts converge in the limit of very low frequencies. As nonlinear modes never suffer hybridizations, our result implies that the presented theoretical framework constitutes a robust alternative definition of `soft glassy modes' in the thermodynamic limit, in which Goldstone modes overwhelm and destroy the identity of low-frequency harmonic glassy modes.

Ontology / Topics

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Glasses Goldstone modes Nonlinear modes

Published as SciPost Phys. 1, 016 (2016)

List of changes

1. We have fixed the mistake in the caption of Fig.1 (horizontal -> vertical).

2. We have expanded the discussion about the dependence of NGM stiffnesses on their order n.

3. We have expanded in the discussion section on how the mild dependence of NGMs’ structural and energetic properties on their order is, in fact, a strength of our approach and not a weakness, as it is expected to facilitate the construction of detection algorithms of the entire field of NGMs.

4. We have clarified our choice of using the non-affine displacement fields as ancestral modes for calculating NGMs with frequencies in the vicinity of the lowest Goldstone modes’ frequencies.

Submission & Refereeing History

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Resubmission 1610.03410v2 on 21 December 2016

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