Diffusion in inhomogeneous media

Martin

et al. 2019

J. High Energ. Phys.

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We consider holographic theories at finite temperature in which a continuous global symmetry in the bulk is spontaneously broken. We study the linear response of operators in a regime which is dual to time dependent, long wavelength deformations of solutions generated by the symmetry. By computing the boundary theory retarded Green's function we show the existence of a gapless mode with a diffusive dispersion relation. The diffusive character of the mode is compatible with the absence of a conserved charge from the field theory point of view. We give an analytic expression for the corresponding diffusion constant in terms of thermodynamic data and a new transport coefficient σ b which is fixed by the black hole horizon data. After adding a perturbative source on the boundary, we compute the resulting gap δω g as a simple function of σ b and of data of the thermal state. arXiv:1905.00398v2 [hep-th] 14 May 20191 Global symmetries are expected to be broken in a quantum theory of gravity [8,9] Nevertheless, they are perfectly well-behaved in the classical low-energy limit.2 Among other results, the authors of [10] considered the hydrodynamic limit of Green's functions in the case of gauged symmetry breaking in the bulk up to linear order in the wavenumber giving a holographic calculation of the speed of sound.

Section: Discussionmentioning

confidence: 99%

Hydrodynamics of broken global symmetries in the bulk

Martin

et al. 2019

J. High Energ. Phys.

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“…Another direction we are working on [42] is the inclusion of a constant magnetic field on the boundary. The resulting Hall angle from the response electric currents is a topic of interest in the literature of the cuprate superconductors.…”

Section: Discussion and Future Directionsmentioning

confidence: 99%

Holographic transport and density waves

2019

J. High Energ. Phys.

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We consider transport of heat and charge in holographic lattices which are phases of strongly coupled matter in which translations are broken explicitly. In these systems, we study a spontaneous density wave that breaks translations incommensurately to the lattice. The emergent gapless mode due to symmetry breaking couples to the heat current impacting transport at low frequencies. We study the effects of this coupling when the mode is freely sliding as well as after the introduction of a small deformation parameter which pins down the density wave. We prove that the DC transport coefficients are discontinuous in the limit of the pinning parameter going to zero. From the perspective of finite frequency thermoelectric conductivity, this limiting process is accompanied by the transfer of spectral weight to frequencies set by the pinning parameter. As expected, for weak momentum relaxation, this spectral weight transfer appears as a shift of the Drude peak. arXiv:1903.05114v3 [hep-th]

“…At temperatures higher than then critical one, hydrodynamics is dictated by the only conserved quantities of the system which are related to time translations and the electric charge. In this regime, the long wavelength excitations are effectively described by incoherent hydrodynamics [16,17]. A good set of local variables which capture the dynamics of these excitations are the local temperature and chemical potential.…”

Section: Introductionmentioning

confidence: 99%

“…Note in particular that relativistic systems with weak momentum relaxation can be described by using relativistic hydrodynamics with perturbative deformations which break translations [17,18]. In that context, the local fluid velocity can be integrated out as a result of momentum relaxation; this was discussed in [17] from the field theory perspective and in [19] within holography. The advantage of the class of models we will consider in our paper is that the momentum relaxation mechanisms will not have to be perturbatively small.…”

Section: Introductionmentioning

confidence: 99%

Incoherent hydrodynamics and density waves

Martin

et al. 2020

Class. Quantum Grav.

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We consider thermal phases of holographic lattices at finite chemical potential in which a continuous internal bulk symmetry can be spontaneously broken. In the normal phase, translational symmetry is explicitly broken by the lattice and the only conserved quantities are related to time translations and the electric charge. The long wavelength excitations of the corresponding charge densities are described by incoherent hydrodynamics yielding two perturbative modes which are diffusive. In the broken phase an additional hydrodynamic degree of freedom couples to the local chemical potential and temperature and we write an effective theory describing the coupled system at leading order in a derivative expansion.