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Waking and scrambling in holographic heating up

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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 Ti to the temperature Tf 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 log 2/2πTi, 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 < log 2/2πTi, 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 Ti increases and widens as Tf increases.

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Authors and Affiliations

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

    D. S. Ageev & I. Ya. Aref’eva

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  1. D. S. Ageev
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  2. I. Ya. Aref’eva
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Correspondence to D. S. Ageev.

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

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Ageev, D.S., Aref’eva, I.Y. Waking and scrambling in holographic heating up. Theor Math Phys 193, 1534–1546 (2017). https://doi.org/10.1134/S0040577917100105

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