Chaos in the BMN matrix model
High Energy Physics - Theory
2024-10-17 v2 Mathematical Physics
math.MP
Chaotic Dynamics
Exactly Solvable and Integrable Systems
Abstract
We study classical chaotic motions in the Berenstein-Maldacena-Nastase (BMN) matrix model. For this purpose, it is convenient to focus upon a reduced system composed of two-coupled anharmonic oscillators by supposing an ansatz. We examine three ans\"atze: 1) two pulsating fuzzy spheres, 2) a single Coulomb-type potential, and 3) integrable fuzzy spheres. For the first two cases, we show the existence of chaos by computing Poincar\'e sections and a Lyapunov spectrum. The third case leads to an integrable system. As a result, the BMN matrix model is not integrable in the sense of Liouville, though there may be some integrable subsectors.
Keywords
Cite
@article{arxiv.1503.04594,
title = {Chaos in the BMN matrix model},
author = {Yuhma Asano and Daisuke Kawai and Kentaroh Yoshida},
journal= {arXiv preprint arXiv:1503.04594},
year = {2024}
}
Comments
23 pages, 15 figures, v2: further clarifications and references added