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Fast scramblers and ultrametric black hole horizons

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Abstract

We propose that fast scrambling on finite-entropy stretched horizons can be modeled by a diffusion process on an effective ultrametric geometry. A scrambling time scaling logarithmically with the entropy is obtained when the elementary transition rates saturate causality bounds on the stretched horizon. The so-defined ultrametric diffusion becomes unstable in the infinite-entropy limit. A formally regularized version can be shown to follow a particular case of the Kohlrausch law.

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Authors and Affiliations

  1. Instituto de Física Teórica IFT UAM/CSIC, Universidad Autonoma de Madrid, C. Nicolas Cabrera 1, Cantoblanco, 28049, Madrid, Spain

    José L. F. Barbón

  2. International Institute of Physics, Universidade Federal do Rio Grande do Norte, Campus Universitario Lagoa Nova, C.P 1661, 59012-970, Natal, Brazil

    Javier M. Magán

Authors
  1. José L. F. Barbón
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  2. Javier M. Magán
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Correspondence to José L. F. Barbón.

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ArXiv ePrint: 1306.3873

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Barbón, J.L.F., Magán, J.M. Fast scramblers and ultrametric black hole horizons. J. High Energ. Phys. 2013, 163 (2013). https://doi.org/10.1007/JHEP11(2013)163

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  • DOI: https://doi.org/10.1007/JHEP11(2013)163

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