Chaos in the BMN matrix model
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arXiv
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| Format: | Preprint |
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2015
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| _version_ | 1866916440917934080 |
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| author | Asano, Yuhma Kawai, Daisuke Yoshida, Kentaroh |
| author_facet | Asano, Yuhma Kawai, Daisuke Yoshida, Kentaroh |
| contents | 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 ansätze: 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 Poincaré 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1503_04594 |
| institution | arXiv |
| publishDate | 2015 |
| record_format | arxiv |
| spellingShingle | Chaos in the BMN matrix model Asano, Yuhma Kawai, Daisuke Yoshida, Kentaroh High Energy Physics - Theory Mathematical Physics Chaotic Dynamics Exactly Solvable and Integrable Systems 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 ansätze: 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 Poincaré 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. |
| title | Chaos in the BMN matrix model |
| topic | High Energy Physics - Theory Mathematical Physics Chaotic Dynamics Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/1503.04594 |