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Chaos in the BMN matrix model

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arxiv 1503.04594 v2 pith:B2GMJ2ZZ submitted 2015-03-16 hep-th math-phmath.MPnlin.CDnlin.SI

Yuhma Asano , Daisuke Kawai , Kentaroh Yoshida This is my paper · ORCID
classification hep-thmath-phmath.MPnlin.CDnlin.SI
keywords integrablematrixmodelchaosfuzzyspheressystemanharmonic
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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.

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    The authors derive leading-order radial and angular stability spectra for two spherical BMN membrane configurations and demonstrate that next-to-leading-order couplings transfer dipole and quadrupole instabilities to ...

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