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A Random Unitary Circuit Model for Black Hole Evaporation | | Lorenzo Piroli
; Christoph Sünderhauf
; Xiao-Liang Qi
; | | Date: |
21 Feb 2020 | | Abstract: | Inspired by the Hayden-Preskill protocol for black hole evaporation, we
consider the dynamics of a quantum many-body qudit system coupled to an
external environment, where the time evolution is driven by the continuous
limit of certain $2$-local random unitary circuits. We study both cases where
the unitaries are chosen with and without a conserved $U(1)$ charge and focus
on two aspects of the dynamics. First, we study analytically and numerically
the growth of the entanglement entropy of the system, showing that two
different time scales appear: one is intrinsic to the internal dynamics (the
scrambling time), while the other depends on the system-environment coupling.
In the presence of a $U(1)$ conserved charge, we show that the entanglement
follows a Page-like behavior in time: it begins to decrease in the middle stage
of the "evaporation", and decreases monotonically afterwards. Second, we study
the time needed to retrieve information initially injected in the system from
measurements on the environment qudits. Based on explicit numerical
computations, we characterize such time both when the retriever has control
over the initial configuration or not, showing that different scales appear in
the two cases. | | Source: | arXiv, 2002.9236 | | Services: | Forum | Review | PDF | Favorites | |
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