Exploring Transition from Stability to Chaos through Random Matrices

Autor:	da Silva, Roberto, Prado, Sandra D.
Rok vydání:	2023
Předmět:	Nonlinear Sciences - Chaotic Dynamics Condensed Matter - Statistical Mechanics
Druh dokumentu:	Working Paper
Popis:	This study explores the application of random matrices to track chaotic dynamics within the Chirikov standard map. Our findings highlight the potential of matrices exhibiting Wishart-like characteristics, combined with statistical insights from their eigenvalue density, as a promising avenue for chaos monitoring. Inspired by a technique originally designed for detecting phase transitions in spin systems, we successfully adapt and apply it to identify analogous transformative patterns in the context of the Chirikov standard map. Leveraging the precision previously demonstrated in localizing critical points within magnetic systems in our prior research, our method accurately pinpoints the Chirikov resonance-overlap criterion for the chaos boundary at $K\approx 2.43$, reinforcing its effectiveness. Comment: 10 pages, 6 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2310.04344 Zobrazit plný text záznamu View this record from Arxiv