Fuzzy spheres in stringy matrix models: quantifying chaos in a mixed phase space
We consider a truncation of the BMN matrix model to a configuration of two fuzzy spheres, described by two coupled non-linear oscillators dependent on the mass parameter μ. The classical phase diagram of the system generically (μ ≠ 0) contains three equilibrium points: two centers and a center-saddl...
| Autores: | , , , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2025 |
| País: | España |
| Institución: | Consejo Superior de Investigaciones Científicas (CSIC) |
| Repositorio: | DIGITAL.CSIC. Repositorio Institucional del CSIC |
| OAI Identifier: | oai:dnet:digitalcsic_::bd71c75d46ba53dadc75189a37261600 |
| Acceso en línea: | http://hdl.handle.net/10261/427929 https://www.scopus.com/inward/record.uri?eid=2-s2.0-105007691163&doi=10.1007%2FJHEP06%282025%29031&partnerID=40&md5=797982f3eca5b54b2560ccb6ec7d9410 |
| Access Level: | acceso abierto |
| Palabra clave: | AdS-CFT Correspondence Gauge-Gravity Correspondence M(atrix) Theories |
| Sumario: | We consider a truncation of the BMN matrix model to a configuration of two fuzzy spheres, described by two coupled non-linear oscillators dependent on the mass parameter μ. The classical phase diagram of the system generically (μ ≠ 0) contains three equilibrium points: two centers and a center-saddle; as μ → 0 the system exhibits a pitchfork bifurcation. We demonstrate that the system is exactly integrable in quadratures for μ = 0, while for very large values of μ, it approaches another integrable point characterized by two harmonic oscillators. The classical phase space is mixed, containing both integrable islands and chaotic regions, as evidenced by the classical Lyapunov spectrum. At the quantum level, we explore indicators of early and late time chaos. The eigenvalue spacing is best described by a Brody distribution, which interpolates between Poisson and Wigner distributions; it dovetails, at the quantum level, the classical results and reemphasizes the notion that the quantum system is mixed. We also study the spectral form factor and the quantum Lyapunov exponent, as defined by out-of-time-ordered correlators. These two indicators of quantum chaos exhibit weak correlations with the Brody distribution. We speculate that the behavior of the system as μ → 0 dominates the spectral form factor and the quantum Lyapunov exponent, making these indicators of quantum chaos less effective in the context of a mixed phase space. © The Author(s) 2025. |
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