Thermoelectric DC conductivities and Stokes flows on black hole horizons

Banks, Elliot; Donos, Aristomenis; Gauntlett, Jerome P.

doi:10.1007/jhep10(2015)103

Cited by 80 publications

(263 citation statements)

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“…to all orders in our derivative expansion. 14 These observations are deeply connected to a beautiful recent paper by Donos and Gauntlett [34] (similar ideas have been developed in [35,48,49].). There it was shown that the DC conductivity of quite general holographic models can be understood from solving the forced Navier-Stokes equations for a fluid living on the black hole horizon.…”

Section: Jhep10(2015)078supporting

confidence: 64%

“…The DC constitutive relations that we have derived (4.7) for the boundary quantum field theory are, for our model, just the same as the exact constitutive relation of the horizon fluid in 15 [34,35]. Similarly, our expression for the fluid velocity, (4.9), is identical to that obtained by solving the Navier-Stokes equation on the horizon.…”

Section: Jhep10(2015)078supporting

confidence: 53%

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Magnetotransport from the fluid/gravity correspondence

Blake

2015

J. High Energ. Phys.

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We continue our construction of a hydrodynamical description of a holographic model with broken translation invariance. Using the fluid/gravity correspondence we derive the constitutive relations of the boundary theory in the presence of a magnetic field. This allows us to obtain novel results for the low-frequency magnetothermoelectric response coefficients. We discuss the DC limit of our hydrodynamics in detail, and show that our approach is equivalent to the 'horizon-fluid' of Donos and Gauntlett.

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Section: Jhep10(2015)078supporting

confidence: 64%

Section: Jhep10(2015)078supporting

confidence: 53%

Magnetotransport from the fluid/gravity correspondence

Blake

2015

J. High Energ. Phys.

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“…While all of these dc conductivities are large, κ ij dc and also κ in (3.44) are parametrically smaller as pointed out in [31,34]. Thus, from (3.46) we deduce that one of the frequencies will be proportional to L −1 while the other will be parametrically smaller.…”

Section: ð3:46þmentioning

confidence: 68%

“…In particular, it should be possible to obtain the Einstein relations in terms of the dc conductivities and the thermodynamic susceptibilities. It is now understood how, in general, the thermoelectric dc conductivity of the boundary field theory, when finite, can be obtained in terms of data on the black hole horizon [32,34,37]. Thus, providing one can obtain the susceptibilities in terms of horizon data, one should also be able to extract the Einstein relations.…”

Section: Final Commentsmentioning

confidence: 99%

Diffusion in inhomogeneous media

2017

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The full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-pro t purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. 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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“…Interestingly, though, even for generic ('non-Q') lattices which break translational symmetry in all the spatial dimensions the conductivity can be obtained by solving some linearized, time-independent, and forced Navier-Stokes-type equations of an effective (charged and incompressible) fluid living on the horizon [186][187][188][189], thus extending the 'membrane paradigm' along the lines of the general concept of a fluid-gravity correspondence [190][191][192][193]. The latter allows for a dual description of the bulk gravity theory in terms of the hydrodynamics of a certain boundary fluid whose stress-energy tensor acts as a source for the boundary metric.…”

Section: From Ads/cmt To Holographic Transportmentioning

confidence: 99%

Demystifying the holographic mystique: A critical review

Khveshchenko¹

2016

Lith. J. Phys.

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Thus far, in spite of many interesting developments, the overall progress towards a systematic study and classification of various 'strange' metallic states of matter has been rather limited. To that end, it was argued that a recent proliferation of the ideas of holographic correspondence originating from string theory might offer a possible way out of the stalemate. However, after almost a decade of intensive studies into the proposed extensions of the holographic conjecture to a variety of condensed matter problems, the validity of this intriguing approach remains largely unknown. This discussion aims at ascertaining its true status and elucidating the conditions under which some of its predictions may indeed be right (albeit, possibly, for a wrong reason).Keywords: strongly correlated systems, holographic correspondence, transport theory, strange metals, analogue gravity PACS: 71.27.+a Condensed matter holography: the promiseAmong the outstanding grand problems in condensed matter physics is that of a deeper understanding and classification of the so-called 'strange metals' or compressible non-Fermi liquid (NFL) states of the strongly interacting systems. However, despite all the effort and a plethora of the important and nontrivial results obtained with the use of the traditional techniques, this program still remains far from completion.As an alternate approach, over the past decade there have been numerous attempts inspired by the hypothetical idea of holographic correspondence which originated from string/gravity/high energy theory (where it is known under the acronym AdS/ CFT) to adapt its main concepts to various condensed matter (or, even more generally, quantum manybody) systems at finite densities and temperatures [1][2][3][4][5][6][7].In its original context, the bona fide holographic principle postulates that certain d + 1-dimensional ('boundary') quantum field theories (e. g. the maximally supersymmetric SU(N) gauge theory) may allow for a dual description in terms of a string theory which, upon a proper compactification, amounts to a certain d + 2-dimensional ('bulk') supergravity. Moreover, in the strong coupling limit (characterized in terms of the t'Hooft coupling constant λ = g 2 N >> 1) and for a large rank N > > 1 of the gauge symmetry group, the bulk description can be further reduced down to a weakly fluctuating gravity model which can even be treated semiclassically at the lowest (0th) order of the underlying 1/N-expansion.In the practical applications of the holographic conjecture, the partition function of a strongly interacting boundary theory with the Lagrangian L(ϕ a ) would then be approximated by a saddle-point (classical) value of the bulk action described by the Lagrangian L(g μν ,…) which includes gravity and other fields dual to their boundary counterparts [1][2][3][4][5][6][7][8] (1) evaluated with the use of a fixed background metric ,while any quantum corrections would usually be neglected by invoking the small parameter 1/N.

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Thermoelectric DC conductivities and Stokes flows on black hole horizons

Cited by 80 publications

References 64 publications

Magnetotransport from the fluid/gravity correspondence

Magnetotransport from the fluid/gravity correspondence

Diffusion in inhomogeneous media

Demystifying the holographic mystique: A critical review

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