Acting on operators with a bare dimension ∆ ∼ N 2 the dilatation operator of U( N ) N $$ \mathcal{N} $$ = 4 super Yang-Mills theory defines a 2-local Hamiltonian acting on a graph. Degrees of freedom are associated with the vertices of the graph while edges correspond to terms in the Hamiltonian. The graph has p ∼ N vertices. Using this Hamiltonian, we study scrambling and equilibration in the large N Yang-Mills theory. We characterize the typical graph and thus the typical Hamiltonian. For the typical graph, the dynamics leads to scrambling in a time consistent with the fast scrambling conjecture. Further, the system exhibits a notion of equilibration with a relaxation time, at weak coupling, given by t ∼ ρ λ $$ \frac{\rho }{\lambda } $$ with λ the ’t Hooft coupling.

中文翻译：

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在杨米尔斯争抢

作用于具有裸维 ∆ ∼ N 2 的算子，U( N ) N $$ \mathcal{N} $$ = 4 的膨胀算子定义了一个作用在图上的 2-局部哈密顿量。自由度与图的顶点相关，而边对应于哈密顿量中的项。该图有 p ∼ N 个顶点。使用这个哈密顿量，我们研究了大 N Yang-Mills 理论中的加扰和平衡。我们刻画了典型的图，从而表征了典型的哈密顿量。对于典型的图，动力学导致加扰的时间与快速加扰猜想一致。此外，系统在弱耦合下表现出具有弛豫时间的平衡概念，由 t ∼ ρ λ $$ \frac{\rho }{\lambda } $$ 给出，λ 是 't Hooft 耦合。