We consider entropy generating flows for fluids that achieve a steady state in the presence of a driving electric field. Having chosen one among the space of stationarity constraints that define such flows we show how energy and momentum relaxation are related in the presence of dissipation. Furthermore, we find that if such a fluid obeys Onsager reciprocity then the incoherent conductivity must be identically zero and consequently makes no contribution to the observable AC or DC charge conductivities.

Italy

Andrea Amoretti

Daniel Brattan

Luca Martinoia

Jonas Rongen

Dissipative electrically driven fluids

We consider as a model of Weyl semimetal thermoelectric transport a (3 + 1)-dimensional charged, relativistic and relaxed fluid with a U(1) V  × U(1) A  chiral anomaly. We take into account all possible mixed energy, momentum, electric and chiral charge relaxations, and discover which are compatible with electric charge conservation, Onsager reciprocity and a finite DC conductivity. We find that all relaxations respecting these constraints necessarily render the system open and violate the second law of thermodynamics. We then demonstrate how the relaxations we have found arise from kinetic theory and a modified relaxation time approximation. Our results lead to DC conductivities that differ from those found in the literature opening the path to experimental verification.

France

Ioannis Matthaiakakis

Relaxation terms for anomalous hydrodynamic transport in Weyl semimetals from kinetic theory

In hydrodynamics, for generic relaxations, the stress tensor and <math><mi>U</mi><mo>(</mo><mn>1</mn><mo>)</mo></math> charge current two-point functions are not time-reversal covariant. This remains true even if the Martin-Kadanoff procedure happens to yield Onsager reciprocal correlators. We consider linearized relativistic hydrodynamics on Minkowski space in the presence of energy, <math><mi>U</mi><mo>(</mo><mn>1</mn><mo>)</mo></math> charge, and momentum relaxation. We then show how one can find the minimal relaxed hydrodynamic framework that does yield two-point functions consistent with time-reversal covariance. We claim the same approach naturally applies to boost agnostic hydrodynamics and its limits (e.g., Carrollian, Galilean, and Lifshitz fluids).

Daniel K. Brattan

Restoring time-reversal covariance in relaxed hydrodynamics

We show that literature results claimed for the magnetic field dependence of the longitudinal conductivity in anomalous first-order hydrodynamics are frame dependent at this derivative order. In particular, we focus on (<math><mrow><mn>3</mn><mo>+</mo><mn>1</mn></mrow></math>)-dimensional hydrodynamics in the presence of a constant <math><mi>O</mi><mo>(</mo><mo>∂</mo><mo>)</mo></math> magnetic field with a <math><mi>U</mi><mo>(</mo><mn>1</mn><mo>)</mo></math> chiral anomaly and demonstrate that, for constitutive relations up to and including order one in derivatives, the anomaly drops out of the longitudinal conductivity. In particular, magnetic field dependent terms that were previously found in the literature only enter the nonzero frequency thermoelectric conductivities through explicitly frame dependent pieces indicating that they are not physical. This issue can be avoided entirely by incorporating the magnetic field into the fluid’s equilibrium state.

Leading order magnetic field dependence of conductivities in anomalous hydrodynamics

Existing hydrodynamic models of charged fluids consider any external electric field acting on the fluid as either first order in the hydrodynamic derivative expansion and completely arbitrary or zeroth order but constrained by the fluid’s chemical potential. This is in tension with experiments on charged fluids, where the electric field is both zeroth order and completely arbitrary. In this work, we take the first step at resolving this conundrum by introducing a new class of hydrodynamic stationary states, including an arbitrary zeroth order electric field, upon which hydrodynamics can be built. We achieve this by first writing down the hydrostatic constitutive relations for a boost-agnostic charged fluid up to first order in derivatives. Then we introduce suitable energy and momentum relaxation terms to balance the influence of the electric field on the fluid. This analysis leads to a new hydrostatic constraint on the spatial fluid velocity, which can be used to define our class of states. This constraint generalizes to the realm of hydrodynamics a similar constraint on the velocity found in the Drude model of electronic transport. Our class of states exhibits non-trivial thermo-electric transport even at ideal order, since it hosts non-zero DC electric and heat currents. We derive the explicit form of the corresponding conductivities and show they depend non-linearly on the electric field.

Non-dissipative electrically driven fluids

We employ hydrodynamics and gauge/gravity to study magneto-transport in phases of matter where translations are broken (pseudo-)spontaneously. First we provide a hydrodynamic description of systems where translations are broken homogeneously at nonzero lattice pressure and magnetic field. This allows us to determine analytic expressions for all the relevant transport coefficients. Next we construct holographic models of those phases and determine all the DC conductivities in terms of the dual black hole geometry. Combining the hydrodynamic and holographic descriptions we obtain analytic expression for the AC thermo-electric correlators. These are fixed in terms of the black hole geometry and a pinning frequency we determine numerically. We find an excellent agreement between our hydrodynamic and holographic descriptions and show that the holographic models are good avatars for the study of magneto-phonons.

Spain

Daniel Areán

Hydrodynamic magneto-transport in holographic charge density wave states

In this paper we study the dynamical properties of charged systems immersed in an external magnetic field and perturbed by a set of scalar operators breaking translations either spontaneously or pseudo-spontaneously. By combining hydrodynamic and quantum field theory arguments we provide analytic expressions for all the hydrodynamic transport coefficients relevant for the diffusive regime in terms of thermodynamic quantities and DC thermo-electric conductivities. This includes the momentum dissipation rate. We shed light on the role of the momentum dissipation rate in the transition between the pseudo-spontaneous and the purely explicit regimes in this class of systems. Finally, we clarify several relations between the hydrodynamic transport coefficients which have been observed in the holographic literature of charge density wave models.

Nicodemo Magnoli

Hydrodynamic magneto-transport in charge density wave states

In this paper we have considered the 3D Ising model perturbed with the energy operator coupled with a nonuniform harmonic potential acting as a trap, showing that this system satisfies the trap-size scaling behavior. Eventually, we have computed the correlators <math><mo>⟨</mo><mi>σ</mi><mo>(</mo><mi>z</mi><mo>)</mo><mi>σ</mi><mo>(</mo><mn>0</mn><mo>)</mo><mo>⟩</mo></math>, <math><mo>⟨</mo><mi>ε</mi><mo>(</mo><mi>z</mi><mo>)</mo><mi>ε</mi><mo>(</mo><mn>0</mn><mo>)</mo><mo>⟩</mo></math> and <math><mo>⟨</mo><mi>σ</mi><mo>(</mo><mi>z</mi><mo>)</mo><mi>ε</mi><mo>(</mo><mn>0</mn><mo>)</mo><mo>⟩</mo></math> near the critical point by means of conformal perturbation theory. Combining this result with Monte Carlo simulations, we have been able to estimate the OPE coefficients <math><msubsup><mi>C</mi><mrow><mi>σ</mi><mi>ε</mi></mrow><mi>σ</mi></msubsup></math>, <math><msubsup><mi>C</mi><mrow><mi>σ</mi><mi>σ</mi></mrow><mi>ε</mi></msubsup></math> and <math><msubsup><mi>C</mi><mrow><mi>ε</mi><mi>ε</mi></mrow><mi>ε</mi></msubsup></math>, finding a good agreement with the values obtained in [G. Costagliola, Phys. Rev. D 93, 066008 (2016), F. Kos, D. Poland, D. Simmons-Duffin, and A. Vichi, J. High Energy Phys. 08 (2016) 036].

Switzerland

Gianluca Costagliola

Marcello Scanavino

Energy trapped Ising model

We consider magnetohydrodynamics with an external magnetic field. We find that in general one must allow for a non-zero incoherent Hall conductivity to correctly describe the DC longitudinal and Hall thermal conductivities beyond order zero in the magnetic field expansion. We apply our result to the dyonic black hole, determining the incoherent Hall conductivity in that case, and additionally prove that the existence of this transport coefficient leads to a significantly better match between the hydrodynamic and AC thermo-electric correlators.

Magneto-thermal transport implies an incoherent Hall conductivity

We study a holographic model where translations are both spontaneously and explicitly broken, leading to the presence of (pseudo)-phonons in the spectrum. The weak explicit breaking is due to two independent mechanisms: a small source for the condensate itself and additional linearly space-dependent marginal operators. The low energy dynamics of the model is described by Wigner crystal hydrodynamics. In absence of a source for the condensate, the phonons remain gapless, but momentum is relaxed. Turning on a source for the condensate damps and pins the phonons. Finally, we verify that the universal relation between the phonon damping rate, mass and diffusivity reported in [1] continues to hold in this model for weak enough explicit breaking.