Fuzzy spheres in stringy matrix models: quantifying chaos in a mixed phase space
Abstract 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 cen...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2025-06-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP06(2025)031 |
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| author | Paolo Amore Leopoldo A. Pando Zayas Juan F. Pedraza Norma Quiroz César A. Terrero-Escalante |
| author_facet | Paolo Amore Leopoldo A. Pando Zayas Juan F. Pedraza Norma Quiroz César A. Terrero-Escalante |
| author_sort | Paolo Amore |
| collection | DOAJ |
| description | Abstract 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. |
| format | Article |
| id | doaj-art-97e5931d0e5a42c6b0a1fd0d50dea44c |
| institution | Kabale University |
| issn | 1029-8479 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj-art-97e5931d0e5a42c6b0a1fd0d50dea44c2025-08-20T03:42:45ZengSpringerOpenJournal of High Energy Physics1029-84792025-06-012025613410.1007/JHEP06(2025)031Fuzzy spheres in stringy matrix models: quantifying chaos in a mixed phase spacePaolo Amore0Leopoldo A. Pando Zayas1Juan F. Pedraza2Norma Quiroz3César A. Terrero-Escalante4Facultad de Ciencias, Universidad de ColimaLeinweber Center for Theoretical Physics, University of MichiganInstituto de Física Teórica UAM/CSICDivisión de Ciencias Exactas, Naturales y Tecnológicas, Centro Universitario del Sur, Universidad de GuadalajaraFacultad de Ciencias, Universidad de ColimaAbstract 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.https://doi.org/10.1007/JHEP06(2025)031AdS-CFT CorrespondenceGauge-Gravity CorrespondenceM(atrix) Theories |
| spellingShingle | Paolo Amore Leopoldo A. Pando Zayas Juan F. Pedraza Norma Quiroz César A. Terrero-Escalante Fuzzy spheres in stringy matrix models: quantifying chaos in a mixed phase space Journal of High Energy Physics AdS-CFT Correspondence Gauge-Gravity Correspondence M(atrix) Theories |
| title | Fuzzy spheres in stringy matrix models: quantifying chaos in a mixed phase space |
| title_full | Fuzzy spheres in stringy matrix models: quantifying chaos in a mixed phase space |
| title_fullStr | Fuzzy spheres in stringy matrix models: quantifying chaos in a mixed phase space |
| title_full_unstemmed | Fuzzy spheres in stringy matrix models: quantifying chaos in a mixed phase space |
| title_short | Fuzzy spheres in stringy matrix models: quantifying chaos in a mixed phase space |
| title_sort | fuzzy spheres in stringy matrix models quantifying chaos in a mixed phase space |
| topic | AdS-CFT Correspondence Gauge-Gravity Correspondence M(atrix) Theories |
| url | https://doi.org/10.1007/JHEP06(2025)031 |
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