Signature of glassy dynamics in dynamic modes decompositions
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , , , |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866913035992432640 |
|---|---|
| author | Nicolaou, Zachary G. Cho, Hangjun Zhang, Yuanzhao Kutz, J. Nathan Brunton, Steven L. |
| author_facet | Nicolaou, Zachary G. Cho, Hangjun Zhang, Yuanzhao Kutz, J. Nathan Brunton, Steven L. |
| contents | Glasses are traditionally characterized by their rugged landscape of disordered low-energy states and their slow relaxation towards thermodynamic equilibrium. Far from equilibrium, dynamical forms of glassy behavior with anomalous algebraic relaxation have also been noted, for example, in networks of coupled oscillators. Due to their disordered and high-dimensional nature, such systems have been difficult to study theoretically, but data-driven methods are emerging as a promising alternative that may aid in their analysis. Here, we characterize glassy dynamics using the dynamic mode decomposition, a data-driven spectral computation that approximates the Koopman spectrum. We show that the gap between oscillatory and decaying modes in the Koopman spectrum vanishes in systems exhibiting algebraic relaxation, and thus, we propose a model-agnostic signature for robustly detecting and analyzing glassy dynamics. We demonstrate the utility of our approach through both a minimal example of a one-dimensional ODE and a high-dimensional example of coupled oscillators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_10918 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Signature of glassy dynamics in dynamic modes decompositions Nicolaou, Zachary G. Cho, Hangjun Zhang, Yuanzhao Kutz, J. Nathan Brunton, Steven L. Disordered Systems and Neural Networks Soft Condensed Matter Statistical Mechanics Pattern Formation and Solitons Glasses are traditionally characterized by their rugged landscape of disordered low-energy states and their slow relaxation towards thermodynamic equilibrium. Far from equilibrium, dynamical forms of glassy behavior with anomalous algebraic relaxation have also been noted, for example, in networks of coupled oscillators. Due to their disordered and high-dimensional nature, such systems have been difficult to study theoretically, but data-driven methods are emerging as a promising alternative that may aid in their analysis. Here, we characterize glassy dynamics using the dynamic mode decomposition, a data-driven spectral computation that approximates the Koopman spectrum. We show that the gap between oscillatory and decaying modes in the Koopman spectrum vanishes in systems exhibiting algebraic relaxation, and thus, we propose a model-agnostic signature for robustly detecting and analyzing glassy dynamics. We demonstrate the utility of our approach through both a minimal example of a one-dimensional ODE and a high-dimensional example of coupled oscillators. |
| title | Signature of glassy dynamics in dynamic modes decompositions |
| topic | Disordered Systems and Neural Networks Soft Condensed Matter Statistical Mechanics Pattern Formation and Solitons |
| url | https://arxiv.org/abs/2502.10918 |