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arXiv · 1902.01912

Holographic Complexity and Charged Scalar Fields

Musema Sinamuli·Robert B. Mann
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Abstract

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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Musema Sinamuli, Robert B. Mann. 2019-02-05. Holographic Complexity and Charged Scalar Fields. https://doi.org/10.1103/physrevd.99.106013

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