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Diffusion in inhomogeneous media.

Donos, Aristomenis and Gauntlett, Jerome P. and Ziogas, Vaios (2017) 'Diffusion in inhomogeneous media.', Physical review D, 96 (12). p. 125003.


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 Uð1Þ 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.

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Publisher statement:Reprinted with permission from the American Physical Society: Donos, Aristomenis, Gauntlett, Jerome P. & Ziogas, Vaios (2017). Diffusion in inhomogeneous media. Physical Review D 96(12): 125003 © 2017 by the American Physical Society. Readers may view, browse, and/or download material for temporary copying purposes only, provided these uses are for noncommercial personal purposes. Except as provided by law, this material may not be further reproduced, distributed, transmitted, modified, adapted, performed, displayed, published, or sold in whole or part, without prior written permission from the American Physical Society.
Date accepted:07 September 2017
Date deposited:05 January 2018
Date of first online publication:11 December 2017
Date first made open access:05 January 2018

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