Chaos in the BMN matrix model

TL;DR

This paper investigates classical chaos in the BMN matrix model by analyzing reduced systems of coupled oscillators, identifying chaotic and integrable regimes through Poincaré sections and Lyapunov spectra.

Contribution

It demonstrates the presence of chaos in the BMN matrix model and identifies integrable subsectors using specific ansätze and dynamical analysis.

Findings

Chaos exists in certain reduced BMN systems.

Integrable subsectors are identified.

The full BMN model is not Liouville integrable.

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.