Publications

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.

The capability of hydrodynamics to accurately describe slow and long-wavelength fluctuations around non-equilibrium steady states, characterized by a stationary flow of energy or matter in the presence of a driving force, remains an open question. In this study, we explicitly construct a hydrodynamic description of electrically driven non-equilibrium charged steady states in the limit in which the relaxation of the first non-hydrodynamic excitation is parametrically slow. Our approach involves introducing gapped modes and extending the effective description into a relaxed hydrodynamic theory. Leveraging gauge-gravity duality as a tool for controlled computations within non-equilibrium systems, we establish an ultraviolet complete model for these steady states that confirms the validity of our relaxed hydrodynamic theory. Our findings provide a concrete realization of the validity of hydrodynamics beyond thermal equilibrium.

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.

In hydrodynamics, for generic relaxations, the stress tensor and U(1) 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 linearised relativistic hydrodynamics on Minkowski space in the presence of energy, U(1) 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, including Carrollian, Galilean and Lifshitz fluids.

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 (3+1)-dimensional hydrodynamics in the presence of a constant first-order magnetic field with a U(1) chiral anomaly and demonstrate that, for constitutive relations up to and including order one in derivatives, the anomaly drops out of the longitudinal conductivity. Magnetic-field-dependent terms previously found in the literature only enter the non-zero-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.

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. We introduce a new class of hydrodynamic stationary states, including an arbitrary zeroth-order electric field, upon which hydrodynamics can be built. We first write down the hydrostatic constitutive relations for a boost-agnostic charged fluid up to first order in derivatives, then introduce suitable energy and momentum relaxation terms to balance the influence of the electric field. This leads to a new hydrostatic constraint on the spatial fluid velocity and to non-trivial thermo-electric transport even at ideal order, with non-zero DC electric and heat currents. We derive the corresponding conductivities and show they depend non-linearly on the electric field.

We uncover a universal relaxation mechanism of pinned density waves using gauge/gravity duality and effective field theory. When translations are spontaneously broken, phonons emerge; weak explicit breaking pins them with a mass and damps them at a computable rate. We show that the damping rate is controlled by the shear modulus, pinning mass and a diffusivity of the purely spontaneous state. At low temperature the collective modes relax quickly into the heat current, so late-time transport is dominated by thermal diffusivity. The resulting resistivity is linear in temperature and the AC conductivity exhibits a transfer of spectral weight from a pinning peak to a Drude-like peak, with possible relevance to cuprate strange metals.

In phases where translations are spontaneously broken, gapless phonons mix at long wavelengths with fluctuations of conserved densities. This mixing is captured by new diffusive transport coefficients and collective modes such as shear sound. Using gauge/gravity duality we model such phases and compute the corresponding diffusivities from black-hole background data. In holographic quantum-critical low-temperature phases we show that these diffusivities are governed by universal relaxation of phonons into the heat current when the dynamical critical exponent exceeds two. We also compute transverse collective modes and find agreement with the shear-sound dispersion of hydrodynamic crystalline solids.