2017/08/31 by Aristomenis Donos, Jerome P. Gauntlett, Vaios Ziogas · 2 citations
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #Composite Material Mechanics #Diffusion #Materials science #Numerical methods in inverse problems #Physics #Statistical physics #Thermodynamics #cond-mat.str-el #hep-th
paper · pdf · doi:10.1103/physrevd.96.125003
published as Phys. Rev. D 96, 125003 (2017) · 33 pages. References added and very minor changes. Published version
arxiv created 2017/12/02 · openalex publication_date 2017/12/11 · arxiv updated 2017/12/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We consider the transport of conserved charges in spatially inhomogeneous quantum systems with a discrete lattice symmetry. We analyze the retarded two-point functions involving the charges and the associated currents at long wavelengths, compared to the scale of the lattice, and, when the dc conductivities are finite, extract the hydrodynamic modes associated with diffusion of the charges. We show that the dispersion relations of these modes are related to the eigenvalues of a specific matrix constructed from the dc conductivities and certain thermodynamic susceptibilities, thus obtaining generalized Einstein relations. We illustrate these general results in the specific context of relativistic hydrodynamics where translation invariance is broken using spatially inhomogeneous and periodic deformations of the stress tensor and the conserved U(1) currents. Equivalently, this corresponds to considering hydrodynamics on a curved manifold, with a spatially periodic metric and chemical potential, and we obtain the dispersion relations for the heat and charge diffusive modes.