#### Time evolution of entanglement entropy of moving mirrors influenced by strongly coupled quantum critical fields

Journal of High Energy Physics
June 2019, 2019:68 | Cite as
Time evolution of entanglement entropy of moving mirrors influenced by strongly coupled quantum critical fields
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Da-Shin LeeChen-Pin Yeh
Open Access
Regular Article - Theoretical Physics
First Online: 14 June 2019
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Abstract
The evolution of the Von Neumann entanglement entropy of a n-dimensional mirror influenced by the strongly coupled d-dimensional quantum critical fields with a dynamic exponent z is studied by the holographic approach. The dual description is a n+1-dimensional probe brane moving in the d+1-dimensional asymptotic Lifshitz geometry ended at r = rb, which plays a role as the UV energy cutoff. Using the holographic influence functional method, we find that in the linear response region, by introducing a harmonic trap for the mirror, which serves as a IR energy cutoff, the Von Neumann entropy at late times will saturate by a power-law in time for generic values of z and n. The saturated value and the relaxation rate depend on the parameter α ≡ 1+(n+2)/z, which is restricted to 1 < α < 3 but α = 2. We find that the saturated values of the entropy are qualitatively different for the theories with 1 < α < 2 and 2 < α < 3. Additionally, the power law relaxation follows the rate ∝ t−2α−1. This probe brane approach provides an alternative way to study the time evolution of the entanglement entropy in the linear response region that shows the similar power-law relaxation behavior as in the studies of entanglement entropies based on Ryu-Takayanagi conjecture. We also compare our results with quantum Brownian motion in a bath of relativistic free fields.
Keywords Gauge-gravity correspondence Holography and condensed matter physics (AdS/CMT) Quantum Dissipative Systems
ArXiv ePrint: 1904.06831
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© The Author(s) 2019
Authors and Affiliations
Da-Shin Lee1Chen-Pin Yeh1Email author1.Department of PhysicsNational Dong-Hwa UniversityHualienTaiwan