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| Paper IPM / Physic / 17168 |
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Motivated by exploring the thermalization process in relativistic and non-relativistic holographic field theories after a non-local quench, we investigate some features in the time evolution of the reflected entropy. This quantity is holographic dual to the entanglement wedge cross section (EWCS) and is related to the entanglement of purification for holographic states. In particular, we focus on its time dependence during black hole formation in $D+2$ dimensional AdS spacetime as well as geometries with Lifshitz and hyperscaling violating exponents. A combination of analytic and numerical results for large symmetric strip shaped boundary subregions shows that the scaling of reflected entropy at early times only depends on Lifshitz exponent. In contrast, this early growth is followed by linear growth whose velocity depends on the dimensions of spacetime, the Lifshitz exponent as well as the hyperscaling parameter. This velocity is the same as the entanglement velocity and for nontrivial dynamical exponent depends on the temperature of the final equilibrium state.
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