标题： 弦论矩阵模型中的模糊球体：在混合相空间中量化混沌 显示英文标题

标题： Fuzzy Spheres in Stringy Matrix Models: Quantifying Chaos in a Mixed Phase Space

摘要： 我们考虑BMN矩阵模型的一个截断配置，由两个模糊球面组成，由两个依赖于质量参数$\mu$的耦合非线性振子描述。 系统的经典相图通常（$\mu \neq 0$）包含三个平衡点：两个中心和一个中心-鞍点；当$\mu \to 0$时，系统表现出叉式分岔。 我们证明该系统在$\mu=0$时可以精确积分，而对于$\mu$的非常大值，它接近由两个谐波振子表征的另一个可积点。 经典的相空间是混合的，包含可积岛和混沌区域，这由经典的李雅普诺夫谱所证实。 在量子层面，我们探讨了早期和晚期时间混沌的指标。 本征值间距最好由布罗迪分布描述，该分布介于泊松分布和威格纳分布之间；在量子层面上，它与经典结果一致，并重新强调了量子系统是混合的这一概念。 我们还研究了谱形因子和由时间有序相关函数定义的量子李雅普诺夫指数。 这两个量子混沌的指标与布罗迪分布存在弱相关性。 我们推测，系统在$\mu \to 0$时的行为主导了谱形因子和量子李雅普诺夫指数，使得这些量子混沌的指标在混合相空间的背景下效果较差。 显示英文摘要

摘要： 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 $\mu$. The classical phase diagram of the system generically ($\mu \neq 0$) contains three equilibrium points: two centers and a center-saddle; as $\mu \to 0$ the system exhibits a pitchfork bifurcation. We demonstrate that the system is exactly integrable in quadratures for $\mu=0$, while for very large values of $\mu$, 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 $\mu \to 0$ 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.