论文标题
随机gue hamiltonians的纠缠动态
Entanglement Dynamics of Random GUE Hamiltonians
论文作者
论文摘要
在这项工作中，我们考虑了一个子系统与水库相互作用和研究纠缠动态的模型，假设总体进化受到不可综合的哈密顿人的控制。我们还与一组可综合的哈密顿人进行了比较。为此，我们利用带有Wigner-Dyson或Poissonian能量分布的随机矩阵的单一不变集合。利用魏因丁函数的理论，我们得出了降低密度矩阵的通用平均时间演变以及纯度，并将这些结果与几个物理汉密尔顿人进行了比较：横向场的随机版本和XXZ模型的随机版本，自旋玻璃，中央旋转和SYK模型。该理论擅长描述后两个。在此过程中，我们发现了Gue Eigenvalues气体中的指数$ n $ n $点相关功能的一般表达式。
In this work, we consider a model of a subsystem interacting with a reservoir and study dynamics of entanglement assuming that the overall time-evolution is governed by non-integrable Hamiltonians. We also compare to an ensemble of Integrable Hamiltonians. To do this, we make use of unitary invariant ensembles of random matrices with either Wigner-Dyson or Poissonian distributions of energy. Using the theory of Weingarten functions, we derive universal average time evolution of the reduced density matrix and the purity and compare these results with several physical Hamiltonians: randomized versions of the transverse field Ising and XXZ models, Spin Glass and, Central Spin and SYK model. The theory excels at describing the latter two. Along the way, we find general expressions for exponential $n$-point correlation functions in the gas of GUE eigenvalues.
