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