Thermoelectric DC conductivities and Stokes flows on black hole horizons

Hyperscaling at the spin density wave quantum critical point in two-dimensional metals

“…These thermodynamic susceptibilities are usually non-critical, and so can be taken to be non-universal and T -independent constants, which depend on the full short-distance structure of the theory. Now we add perturbations associated with umklapp scattering or quenched disorder which can relax the total momentum [5][6][7][8][9][10][11][12][13][14][39][40][41][42][43]: this leads to a momentum relaxation rate Γ which shifts the pole in Eq. (1.4) off the real axis to ω = −iΓ, and so the conductivity takes the finite value at ω = 0…”

Incoherent thermal transport from dirty black holes

“…Recently, the tools to analytically address this problem have been developed. Firstly, the computation of thermal DC conductivity has been reduced to a hydrodynamics problem for an "artificial" fluid on the black hole horizon [22,23]. Secondly, a general hydrodynamic framework has been developed which can provide non-perturbative bounds on transport coefficients [24].…”

“…Although our choice of radial coordinate is a bit different than what is used in [23], since this metric obeys all general constraints demanded in their paper, we may still use their results in our new coordinate system. We assume our boundary theory and black hole horizon have topology T d , and so we can introduce normalized spatial averaging over the horizon, which we denote by…”

“…( 12) allows us to place non-trivial constraints on the possible h ij , and will play a crucial role in finding bounds on κ. One Dimension.-We begin by considering boundary theories with one spatial dimension, where it has recently been shown [23] that given any EMD theory (4): [50]…”

“…Following [24,25], it is straightforward to derive a variational bound on the thermal conductivity. [23] showed that the DC transport coefficients may be computed as follows: solve the following equations…”