# Slowing down of so-called chaotic states: Freezing'' the initial state

3 CPT - Ex E7 Systèmes dynamiques et théorie ergodique
CPT - Centre de Physique Théorique - UMR 7332
Abstract : The so-called chaotic states that emerge on the model of $XY$ interacting on regular critical range networks are analyzed. Typical time scales are extracted from the time series analysis of the global magnetization. The large spectrum confirms the chaotic nature of the observable, anyhow different peaks in the spectrum allows for typical characteristic time-scales to emerge. We find that these time scales {$\tau(N)$} display a critical slowing down, i.e they diverge as $N\rightarrow\infty$. The scaling law is analyzed for different energy densities and the behavior $\tau(N)\sim\sqrt{N}$ is exhibited. This behavior is furthermore explained analytically using the formalism of thermodynamic-equations of the motion and analyzing the eigenvalues of the adjacency matrix.
Type de document :
Article dans une revue
Discontinuity, Nonlinearity, and Complexity, L & H Scientific Publishing, 2016, 5 (4), pp.447-455. 〈https://lhscientificpublishing.com/journals/DNC-Default.aspx〉. 〈10.5890/DNC.2016.12.009〉

https://hal.archives-ouvertes.fr/hal-01303533
Contributeur : Xavier Leoncini <>
Soumis le : lundi 18 avril 2016 - 12:10:18
Dernière modification le : jeudi 15 mars 2018 - 16:56:08

### Citation

Martin Belger, Sarah De Nigris, Xavier Leoncini. Slowing down of so-called chaotic states: Freezing'' the initial state. Discontinuity, Nonlinearity, and Complexity, L & H Scientific Publishing, 2016, 5 (4), pp.447-455. 〈https://lhscientificpublishing.com/journals/DNC-Default.aspx〉. 〈10.5890/DNC.2016.12.009〉. 〈hal-01303533〉

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