Abstract
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.
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Acknowledgments
We would like to acknowledge discussions with Blaise Goutéraux, Ashish Shukla, Watse Sybesma, Benjamin Withers and Vaios Ziogas on the issues presented in this work. We would like to give special thanks to Jonas Ludovico Rongen for explicitly checking our calculations of the constitutive relations and spotting several typos in the appendices of previous versions of this work. A.A. and I.M. have been partially supported by the “Curiosity Driven Grant 2020” of the University of Genoa and the INFN Scientific Initiative SFT: “Statistical Field Theory, Low-Dimensional Systems, Integrable Models and Applications”. This project has also received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No. 101030915.
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Amoretti, A., Brattan, D.K., Martinoia, L. et al. Non-dissipative electrically driven fluids. J. High Energ. Phys. 2023, 218 (2023). https://doi.org/10.1007/JHEP05(2023)218
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DOI: https://doi.org/10.1007/JHEP05(2023)218