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Introduction
The holographic duality provides a unique method to investigate the dynamics of strongly coupled field theories, which links geometrical quantities to quantum observables. The uses of this interplay to study thermal phases of strongly coupled field theories by their holographically dual AdS black hole/brane geometries have attracted lots of attention since it was first porposed. It was then suggested that the small perturbations of the AdS metric are dual to the hydrodynamics or linear response theories of the boundary CFTs. Also, by probed strings in the AdS background, the diffusion behavior of Brownian particles in the boundary fields can be derived. In particular, the time evolution of entanglement entropy between Brownian particles and boundary fields had been studied by means of the probed string method.