论文标题
质量变形ABJM模型的混沌动力学
Chaotic Dynamics of the Mass Deformed ABJM Model
论文作者
论文摘要
我们探讨了大规模成型的Aharony-Bergman-Jafferis-Maldacena模型的混乱动态。为此，考虑到该字段在空间上是统一的，我们首先将该模型从$ 2+1 $降低到$ 0+1 $尺寸。在涉及模糊的2个角度的ANSATZ配置中进行'T Hooft限制和追踪，这些配置是用Gomis-Rodriguez-gomez-van raamsdonk-verlinde矩阵和集体时间依赖性的Gomis-Rodriguez-van raamsdonk-verlinde矩阵进行了描述的，我们获得了有效的lagrangians and exply feckun and collept liapt的家族，以证明与之相关的动力学。特别是，我们专注于最大的Lyapunov指数（$λ_l$）如何随$ e/n^2 $的函数而变化。 Depending on the structure of the effective potentials, we find either $λ_L \propto (E/N^2)^{1/3}$ or $λ_L \propto (E/N^2 - γ_N)^{1/3}$, where $γ_N(k, μ)$ are constants determined in terms of the Chern-Simons coupling $k$, the mass $μ$, and the matrix level $ n $。指出经典的动力学仅在高温方向上仅在量子理论上近似，我们研究了最大的Lyapunov指数的温度依赖性，并在温度下给出上限，$λ_l$值符合Maldacena-Shenker-Stanford符合Maldacena-Shenker-Stanford，$λ_l\λ_l\λ_l\ leq2πt$，最终将不适合使用。
We explore the chaotic dynamics of the mass-deformed Aharony-Bergman-Jafferis-Maldacena model. To do so, we first perform a dimensional reduction of this model from $2+1$ to $0+1$ dimensions, considering that the fields are spatially uniform. Working in the 't Hooft limit and tracing over ansatz configurations involving fuzzy 2-spheres, which are described in terms of the Gomis-Rodriguez-Gomez-Van Raamsdonk-Verlinde matrices with collective time dependence, we obtain a family of reduced effective Lagrangians and demonstrate that they have chaotic dynamics by computing the associated Lyapunov exponents. In particular, we focus on how the largest Lyapunov exponent, $λ_L$, changes as a function of $E/N^2$. Depending on the structure of the effective potentials, we find either $λ_L \propto (E/N^2)^{1/3}$ or $λ_L \propto (E/N^2 - γ_N)^{1/3}$, where $γ_N(k, μ)$ are constants determined in terms of the Chern-Simons coupling $k$, the mass $μ$, and the matrix level $N$. Noting that the classical dynamics approximates the quantum theory only in the high-temperature regime, we investigate the temperature dependence of the largest Lyapunov exponents and give upper bounds on the temperature above which $λ_L$ values comply with the Maldacena-Shenker-Stanford bound, $ λ_L \leq 2 πT $, and below which it will eventually be not obeyed.
