Diffusion in inhomogeneous media

Donos, Aristomenis; Gauntlett, Jerome P.; Ziogas, Vaios

Abstract

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.

Citation

Donos, A., Gauntlett, J. P., & Ziogas, V. (2017). Diffusion in inhomogeneous media. Physical Review D, 96(12), Article 125003. https://doi.org/10.1103/physrevd.96.125003

• Journal Article Type: Article
• Acceptance Date: Sep 7, 2017
• Online Publication Date: Dec 11, 2017
• Publication Date: Dec 11, 2017
• Deposit Date: Jan 5, 2018
• Publicly Available Date: Jan 5, 2018
• Journal: Physical Review D
• Print ISSN: 2470-0010
• Electronic ISSN: 2470-0029
• Publisher: American Physical Society
• Peer Reviewed: Peer Reviewed
• Volume: 96
• Issue: 12
• Article Number: 125003
• DOI: https://doi.org/10.1103/physrevd.96.125003
• Public URL: https://durham-repository.worktribe.com/output/1368834