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arXiv 1902.01912hep-th
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全息复杂性与带电标量场

Holographic Complexity and Charged Scalar Fields

Musema Sinamuli, Robert B. Mann

摘要:

我们构造了一个量子系统的计算复杂性的时间依赖的表达式,该量子系统由两个d维共形复标量场理论耦合到常数电势,并定义在(d+1)维带电AdS黑洞的边界上。使用一个合适的选择的参考状态,哈密顿门和度量的酉流形上,我们发现,复杂性线性增长的一个相对较大的时间间隔。我们还注意到,对于电荷非常小的标量场,复杂度的变化率不能超过一个最大值,称为劳埃德界。

英文摘要:

We construct a time-dependent expression of the computational complexity of a quantum system which consists of two conformal complex scalar field theories in d dimensions coupled to constant electric potentials and defined on the boundaries of a charged AdS black hole in (d+1) dimensions. Using a suitable choice of the reference state, Hamiltonian gates and the metric on the manifold of unitaries, we find that the complexity grows linearly for a relatively large interval of time. We also remark that for scalar fields with very small charges the rate of variation of the complexity cannot exceed a maximum value known as the Lloyd bound.

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