Thermoelectric conductivities at finite magnetic field and the Nernst effect

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Abstract:We study diffusion and butterfly velocity (v B ) in two holographic models, linear axion and axion-dilaton model, with a momentum relaxation parameter (β) at finite density or chemical potential (µ). Axion-dilaton model is particularly interesting since it shows linear-T -resistivity, which may have something to do with the universal bound of diffusion. At finite density, there are two diffusion constants D ± describing the coupled diffusion of charge and energy. By computing D ± exactly, we find that in the incoherent regime (β/T 1, β/µ 1) D + is identified with the charge diffusion constant (D c ) and D − is identified with the energy diffusion constant (D e ). In the coherent regime, at very small density, D ± are 'maximally' mixed in the sense that D + (D − ) is identified with D e (D c ), which is opposite to the case in the incoherent regime. In the incoherent regime D e ∼ C − v 2 B /k B T where C − = 1/2 or 1 so it is universal independently of β and µ. However, D c ∼ C + v 2 B /k B T where C + = 1 or β 2 /16π 2 T 2 so, in general, C + may not saturate to the lower bound in the incoherent regime, which suggests that the characteristic velocity for charge diffusion may not be the butterfly velocity. We find that the finite density does not affect the diffusion property at zero density in the incoherent regime.

Section: Butterfly Velocitymentioning

confidence: 89%

Diffusion and butterfly velocity at finite density

Niu

Kim

2017

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“…Secondly, since our description differs from that presented in [2], it is natural to revisit the motivating questions of that work. Through applying the fluid/gravity correspondence in a magnetic field we could construct a theory of magnetotransport [29][30][31][32] and study the frequency dependence of the Hall angle [33].…”

Section: Discussionmentioning

confidence: 99%

Momentum relaxation from the fluid/gravity correspondence

Blake

2015

We provide a hydrodynamical description of a holographic theory with broken translation invariance. We use the fluid/gravity correspondence to systematically obtain both the constitutive relations for the currents and the Ward identity for momentum relaxation in a derivative expansion. Beyond leading order in the strength of momentum relaxation, our results differ from a model previously proposed by Hartnoll et al. As an application of these techniques we consider charge and heat transport in the boundary theory. We derive the low frequency thermoelectric transport coefficients of the holographic theory from the linearised hydrodynamics.

“…Building on [1], a number of recent articles have revisited the problem of magnetotransport with momentum relaxation by computing the thermoelectric and Hall conductivities either holographically [5,[33][34][35] or with memory matrices [8]. To resolve the discrepancy between the hydrodynamic, memory matrix, and holographic DC calculations, it would be worthwhile to adapt our techniques to calculate the frequency dependent conductivities at non-zero B.…”

Section: Jhep09(2015)090 4 Outlookmentioning

confidence: 99%

Dissecting holographic conductivities

Davison

Goutéraux

2015

110

135

Abstract:The DC thermoelectric conductivities of holographic systems in which translational symmetry is broken can be efficiently computed in terms of the near-horizon data of the dual black hole. By calculating the frequency dependent conductivities to the first subleading order in the momentum relaxation rate, we give a physical explanation for these conductivities in the simplest such example, in the limit of slow momentum relaxation. Specifically, we decompose each conductivity into the sum of a coherent contribution due to momentum relaxation and an incoherent contribution, due to intrinsic current relaxation. This decomposition is different from those previously proposed, and is consistent with the known hydrodynamic properties in the translationally invariant limit. This is the first step towards constructing a consistent theory of charged hydrodynamics with slow momentum relaxation.