Diffusion for Holographic Lattices
arXiv:1710.04221 · doi:10.1007/JHEP03(2018)056
Abstract
We consider black hole spacetimes that are holographically dual to strongly coupled field theories in which spatial translations are broken explicitly. We discuss how the quasinormal modes associated with diffusion of heat and charge can be systematically constructed in a long wavelength perturbative expansion. We show that the dispersion relation for these modes is given in terms of the thermoelectric DC conductivity and static susceptibilities of the dual field theory and thus we derive a generalised Einstein relation from Einstein's equations. A corollary of our results is that thermodynamic instabilities imply specific types of dynamical instabilities of the associated black hole solutions.
36 pages; very minor changes, published version
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- Incoherent hydrodynamics and density waves
- Hydrodynamics of broken global symmetries in the bulk
- Boomerang RG flows with intermediate conformal invariance
- U(1) quasi-hydrodynamics: Schwinger-Keldysh effective field theory and holography
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- Non-equilibrium dynamics in Holography