Relativistic fluids are Lorentz invariant, and a non-relativistic limit of such fluids leads to the well-known Navier-Stokes equation. However, for fluids moving with respect to a reference system, or in critical systems with generic dynamical exponent z, the assumption of Lorentz invariance (or its non-relativistic version) does not hold. We are thus led to consider the most general fluid assuming only homogeneity and isotropy and study its hydrodynamics and transport behaviour. Remarkably, such systems have not been treated in full generality in the literature so far. Here we study these equations at the linearized level. We find new expressions for the speed of sound, corrections to the Navier-Stokes equation and determine all dissipative and non-dissipative first order transport coefficients. Dispersion relations for the sound, shear and diffusion modes are determined to second order in momenta. In the presence of a scaling symmetry with dynamical exponent z, we show that the sound attenuation constant depends on both shear viscosity and thermal conductivity.
Cited by 3
Masaru Hongo, Nonrelativistic Hydrodynamics from Quantum Field Theory: (I) Normal Fluid Composed of Spinless Schrödinger Fields
J Stat Phys 174, 1038 (2019) [Crossref]
Markus Garbiso et al., Dispersion relations in non-relativistic two-dimensional materials from quasinormal modes in Hǒrava Gravity
J. High Energ. Phys. 2019, 87 (2019) [Crossref]
Richard A. Davison et al., Impact of irrelevant deformations on thermodynamics and transport in holographic quantum critical states
Phys. Rev. D 100, 086020 (2019) [Crossref]
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- 1 Institute of Physics, University of Amsterdam [IoP, UvA]
- 2 Københavns Universitet / University of Copenhagen [UCPH]
- 3 Universiteit Utrecht / University of Utrecht [UU]