Abstract
We examine the complexity of quasi-static chaotic open quantum systems. As a prototypical example, we analytically compute the Krylov complexity of a slowly leaking hard-sphere gas using Berry’s conjecture. We then connect it to the holographic complexity of a d + 1-dimensional evaporating black hole using the Complexity=Volume proposal. We model the black hole spacetime by stitching together a sequence of static Schwarzschild patches across incoming negative energy null shock waves. Under certain identification of parameters, we find the late time complexity growth rate during each quasi-static equilibrium to be the same in both systems.
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Acknowledgments
I thank Friðrik Freyr Gautason, Chethan Krishnan, Watse Sybesma, and Lárus Thorlacius for their insights and helpful discussions. This work was supported by the Icelandic Research Fund grant 228952-052.
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Mohan, V. Krylov complexity of open quantum systems: from hard spheres to black holes. J. High Energ. Phys. 2023, 222 (2023). https://doi.org/10.1007/JHEP11(2023)222
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DOI: https://doi.org/10.1007/JHEP11(2023)222