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Transport Coefficients for Holographic Hydrodynamics at Finite Energy Scale
We investigate the relations between black hole thermodynamics and
holographic transport coefficients in this paper. The formulae for DC
conductivity and diffusion coefficient are verified for electrically
single-charged black holes. We examine the correctness of the proposed
expressions by taking charged dilatonic and single-charged STU black holes as
two concrete examples, and compute the flows of conductivity and diffusion
coefficient by solving the linear order perturbation equations. We then check
the consistence by evaluating the Brown-York tensor at a finite radial
position. Finally, we find that the retarded Green functions for the shear
modes can be expressed easily in terms of black hole thermodynamic quantities
and transport coefficients.Comment: 33 pages,4 figures,to appear in Advances in High Energy Physic
Closed-loop control of complex networks : A trade-off between time and energy
W. L. is supported by the National Science Foundation of China (NSFC) (Grants No. 11322111 and No. 61773125). Y.-Z. S. is supported by the NSFC (Grant No. 61403393). Y.-C. L. acknowledges support from the Vannevar Bush Faculty Fellowship program sponsored by the Basic Research Office of the Assistant Secretary of Defense for Research and Engineering and funded by the Office of Naval Research through Grant No. N00014-16-1-2828. Y.-Z. S. and S.-Y. L. contributed equally to this work.Peer reviewedPublisher PD
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