论文标题
矩阵量规理论中的混乱和大量变形
Chaos in Matrix Gauge Theories with Massive Deformations
论文作者
论文摘要
从具有大量变形项的$ su（n）$矩阵量子力学模型开始，然后引入ANSATZ配置，涉及涉及模糊的四个角度和二角列，我们获得了有效的汉密尔顿人的家族，$ h_n \，$ h_n \ ,,（n = \ frac {1}} n} n+1}（n+1）（N+1）（N+1）（N+2）混乱的动力学。通过数值工作，我们将最大的Lyapunov指数的变化建模为能量的函数，并发现它们的变化是$ \ propto（e-（e_n）_f）^{1/4} $或$ \ propto e^{1/4} $，其中$（e_n）_f $ for dourgies ofergies的阶段的空间，我们使用结果将上限放在高于Lyapunov指数符合Maldacena-Shenker-Stanford（MSS）限制的$2πt$的温度下，最终将被违反。
Starting from an $SU(N)$ matrix quantum mechanics model with massive deformation terms and by introducing an ansatz configuration involving fuzzy four- and two-spheres with collective time dependence, we obtain a family of effective Hamiltonians, $H_n \,, (N = \frac{1}{6}(n+1)(n+2)(n+3))$ and examine their emerging chaotic dynamics. Through numerical work, we model the variation of the largest Lyapunov exponents as a function of the energy and find that they vary either as $\propto (E-(E_n)_F)^{1/4} $ or $\propto E^{1/4}$, where $(E_n)_F$ stand for the energies of the unstable fixed points of the phase space. We use our results to put upper bounds on the temperature above which the Lyapunov exponents comply with the Maldacena-Shenker-Stanford (MSS) bound, $2 πT $, and below which it will eventually be violated.
