Chaos in the BMN matrix model

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 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.

23 pages, 15 figures, v2: further clarifications and references added

References in corpus (6)

• A bound on chaos
• Chaos Rules out Integrability of Strings in AdS_5 x T^{1,1}
• On (non)integrability of classical strings in p-brane backgrounds
• Non-integrability in non-relativistic theories
• Classical Solutions in the BMN Matrix Model
• Chaos in Lifshitz Spacetimes

Cited by in corpus (28)

• Exponential growth of out-of-time-order correlator without chaos: inverted harmonic oscillator
• Chaos in Classical D0-Brane Mechanics
• Integrability and non-Integrability in N=2 SCFTs and their Holographic Backgrounds
• The non-Integrability of Strings in Massive Type IIA and their Holographic duals
• Chaotic strings in a near Penrose limit of AdS${}_5\times T^{1,1}$
• Chaos in chiral condensates in gauge theories
• Non-integrability on AdS${}_3$ supergravity backgrounds
• The fate of chaotic strings in a confining geometry
• Universality in Chaos: Lyapunov Spectrum and Random Matrix Theory
• Chaos in classical string dynamics in $\hat{\gamma }$ deformed $Ad{S}_5\times T^{1,1}$
• Chaos of QCD string from holography
• The smallest matrix black hole model in the classical limit
• Chaotic spin chains in AdS/CFT
• Probing analytical and numerical integrability: The curious case of $(Ad{S}_5\times S^5{)}_{\eta }$
• Classical and quantum butterfly effect in nonlinear vector mechanics
• Analytic Non-Integrability and S-Matrix Factorization
• Chaotic instability in the BFSS matrix model
• Chaos in $SU(2)$ Yang-Mills Chern-Simons Matrix Model
• Phantoms and strange attractors in cosmology
• Multipole Stability of Spinning M2-branes in the Classical Limit of the BMN Matrix Model
• Chaos from Equivariant Fields on Fuzzy $S^4$
• Chaotic Dynamics of the Mass Deformed ABJM Model
• Chaos from Massive Deformations of Yang-Mills Matrix Models
• Chaos in balanced and unbalanced holographic s+p superconductors
• Thermalization in massive deformations of Yang-Mills matrix models
• Spinning the Fuzzy Sphere
• M-theory as a dynamical system generator
• Non-Integrability of Strings in $Ad{S}_6\times S^2\times \Sigma$ Background and its 5D Holographic Duals