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 TMF, 2017, Volume 193, Number 1, Pages 146–161 (Mi tmf9337)

Waking and scrambling in holographic heating up

D. S. Ageev, I. Ya. Aref'eva

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia

Abstract: Using holographic methods, we study the heating up process in quantum field theory. As a holographic dual of this process, we use absorption of a thin shell on a black brane. We find the explicit form of the time evolution of the quantum mutual information during heating up from the temperature $T_{\mathrm i}$ to the temperature $T_{\mathrm f}$ in a system of two intervals in two-dimensional space–time. We determine the geometric characteristics of the system under which the time dependence of the mutual information has a bell shape: it is equal to zero at the initial instant, becomes positive at some subsequent instant, further attains its maximum, and again decreases to zero. Such a behavior of the mutual information occurs in the process of photosynthesis. We show that if the distance $x$ between the intervals is less than $\ln 2/2\pi T_{\mathrm i}$, then the evolution of the holographic mutual information has a bell shape only for intervals whose lengths are bounded from above and below. For sufficiently large $x$, i.e., for $x>\ln2/2\pi T_{\mathrm i}$, the bell-like shape of the time dependence of the quantum mutual information is present only for sufficiently large intervals. Moreover, the zone narrows as $T_{\mathrm i}$ increases and widens as $T_{\mathrm f}$ increases.

Keywords: AdS/CFT correspondence, holography, mutual information, entanglement entropy, scrambling, wake-up, heating up, thermalization, photosynthesis.

 Funding Agency Grant Number Russian Science Foundation 14-11-00687 This research was supported by a grant from the Russian Science Foundation (Project No. 14-11-00687).

DOI: https://doi.org/10.4213/tmf9337

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English version:
Theoretical and Mathematical Physics, 2017, 193:1, 1534–1546

Bibliographic databases:

ArXiv: 1701.07280

Citation: D. S. Ageev, I. Ya. Aref'eva, “Waking and scrambling in holographic heating up”, TMF, 193:1 (2017), 146–161; Theoret. and Math. Phys., 193:1 (2017), 1534–1546

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/tmf9337
• https://doi.org/10.4213/tmf9337
• http://mi.mathnet.ru/eng/tmf/v193/i1/p146

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Citing articles on Google Scholar: Russian citations, English citations
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This publication is cited in the following articles:
1. I. Ya. Aref'eva, I. V. Volovich, O. V. Inozemcev, “Holographic control of information and dynamical topology change for composite open quantum systems”, Theoret. and Math. Phys., 193:3 (2017), 1834–1843
2. D. S. Ageev, I. Ya. Aref'eva, “Holographic non-equilibrium heating”, J. High Energy Phys., 2018, no. 3, 103
3. I. Ya. Aref'eva, I. V. Volovich, O. V. Inozemtsev, “Evolution of holographic entropy quantities for composite quantum systems”, Theoret. and Math. Phys., 197:3 (2018), 1838–1844
4. M. R. Tanhayi, R. Vazirian, S. Khoeini-Moghaddam, “Complexity growth following multiple shocks”, Phys. Lett. B, 790 (2019), 49–57
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