Late time quantum chaos of pure states in random matrices and in the Sachdev-Ye-Kitaev model
Late time quantum chaos of pure states in random matrices and in the Sachdev-Ye-Kitaev model
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DOI：
10.1103/physrevd.100.126017
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发表时间：
2019-01
影响因子：
5
通讯作者：
Tokiro Numasawa
中科院分区：
文献类型：
--
作者：
Tokiro Numasawa
本文研究了SYK模型中的返回振幅，即初始态和时间演化态之间的重叠。初始状态被认为是自旋基础上的产物状态。通过精确对角化哈密顿量，我们数值研究了返回振幅。我们还推导了随机矩阵理论中反射振幅的解析表达式。SYK的结果与随机矩阵的期望值一致。我们还研究了不同的哈密顿量，最初提出的描述在投影黑洞的全息背景下的可穿越虫洞的时间演化。时间演化现在取决于初始产物状态的选择。结果再次解释了随机矩阵理论。在辛系综的情况下，我们观察到一个有趣的模式的返回幅度，他们显示第二个倾角，斜坡，和高原状的行为。
We study the return amplitude, which is the overlap between the initial state and the time-evolved state, in the Sachdev-Ye-Kitaev (SYK) model. Initial states are taken to be product states in a spin basis. We numerically study the return amplitude by exactly diagonalizing the Hamiltonian. We also derive the analytic expression for the return amplitude in random matrix theory. The SYK results agree with the random matrix expectation. We also study the time evolution under the different Hamiltonian that is originally proposed to describe the traversable wormholes in projected black holes in the context of holography. The time evolution now depends on the choice of initial product states. The results are again explained by random matrix theory. In the symplectic ensemble cases, we observe an interesting pattern of the return amplitude in which they show the second dip, ramp, and plateaulike behavior.