Diffusion in inhomogeneous media - INSPIRE

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Diffusion in inhomogeneous media

Aristomenis Donos
(
- Durham U., CPT and
- Durham U., Dept. of Math.
)
,
Jerome P. Gauntlett
(
- Imperial Coll., London
)
,
Vaios Ziogas
(
- Durham U., CPT and
- Durham U., Dept. of Math.
)

Aug 17, 2017

17 pages

Published in:

Phys.Rev.D 96 (2017) 12, 125003

Published: Dec 11, 2017

e-Print:

1708.05412 [hep-th]

DOI:

10.1103/PhysRevD.96.125003

Report number:

IMPERIAL-TP-2017-JG-04,
DCPT-17-21

View in:

reference search18 citations

Citations per year

Abstract: (APS)

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.

Note:

33 pages. References added and very minor changes. Published version

hydrodynamics: relativistic
charge: conservation law
charge: diffusion
potential: chemical
symmetry: lattice
tensor: energy-momentum
conductivity
dispersion relation
two-point function
thermodynamical

References(51)

Figures(0)

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