Abstract
We construct the general first-order hydrodynamic theory invariant under time translations, the Euclidean group of spatial transformations and preserving particle number, that is with symmetry group ℝt×ISO(d)×U(1). Such theories are important in a number of distinct situations, ranging from the hydrodynamics of graphene to flocking behaviour and the coarse-grained motion of self-propelled organisms. Furthermore, given the generality of this construction, we are able to deduce special cases with higher symmetry by taking the appropriate limits. In this way we write the complete first-order theory of Lifshitz-invariant hydrodynamics. Among other results we present a class of non-dissipative first order theories which preserve parity.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
L.D. Landau and E.M. Lifshitz, Fluid mechanics, second edition, Pergamon, Oxford U.K. (1987).
P. Kovtun, Lectures on hydrodynamic fluctuations in relativistic theories, J. Phys. A 45 (2012) 473001 [arXiv:1205.5040] [INSPIRE].
J. Sonner and B. Withers, Universal spatial structure of nonequilibrium steady states, Phys. Rev. Lett. 119 (2017) 161603 [arXiv:1705.01950] [INSPIRE].
I. Novak, J. Sonner and B. Withers, Overcoming obstacles in nonequilibrium holography, Phys. Rev. D 98 (2018) 086023 [arXiv:1806.08655] [INSPIRE].
B.N. Narozhny, I.V. Gornyi, A.D. Mirlin and J. Schmalian, Hydrodynamic approach to electronic transport in graphene, Annalen Phys. 529 (2017) 1700043 [arXiv:1704.03494].
A. Lucas and K.C. Fong, Hydrodynamics of electrons in graphene, J. Phys. Condens. Matter 30 (2018) 053001 [arXiv:1710.08425] [INSPIRE].
J. Toner, Y. Tu and S. Ramaswamy, Hydrodynamics and phases of flocks, Annals Phys. 318 (2005) 170.
Y. Hatwalne, S. Ramaswamy, M. Rao and R.A. Simha, Rheology of active-particle suspensions, Phys. Rev. Lett. 92 (2004) 118101.
A.C. Callan-Jones and F. Jülicher, Hydrodynamics of active permeating gels, New J. Phys. 13 (2011) 093027.
S. Fürthauer, M. Neef, S.W. Grill, K. Kruse and F. Jülicher, The Taylor-Couette motor: spontaneous flows of active polar fluids between two coaxial cylinders, New J. Phys. 14 (2012) 023001
A. Nicolis, R. Penco, F. Piazza and R. Rattazzi, Zoology of condensed matter: Framids, ordinary stuff, extra-ordinary stuff, JHEP 06 (2015) 155 [arXiv:1501.03845] [INSPIRE].
T. Jacobson and D. Mattingly, Gravity with a dynamical preferred frame, Phys. Rev. D 64 (2001) 024028 [gr-qc/0007031] [INSPIRE].
J. de Boer, J. Hartong, N.A. Obers, W. Sybesma and S. Vandoren, Perfect Fluids, SciPost Phys. 5 (2018) 003 [arXiv:1710.04708] [INSPIRE].
J. de Boer, J. Hartong, N.A. Obers, W. Sybesma and S. Vandoren, Hydrodynamic Modes of Homogeneous and Isotropic Fluids, SciPost Phys. 5 (2018) 014 [arXiv:1710.06885] [INSPIRE].
N. Poovuttikul and W. Sybesma, First order non-Lorentzian fluids, entropy production and linear instabilities, arXiv:1911.00010 [INSPIRE].
J. Bhattacharya, S. Bhattacharyya and M. Rangamani, Non-dissipative hydrodynamics: Effective actions versus entropy current, JHEP 02 (2013) 153 [arXiv:1211.1020] [INSPIRE].
N. Banerjee, J. Bhattacharya, S. Bhattacharyya, S. Jain, S. Minwalla and T. Sharma, Constraints on Fluid Dynamics from Equilibrium Partition Functions, JHEP 09 (2012) 046 [arXiv:1203.3544] [INSPIRE].
K. Jensen, M. Kaminski, P. Kovtun, R. Meyer, A. Ritz and A. Yarom, Towards hydrodynamics without an entropy current, Phys. Rev. Lett. 109 (2012) 101601 [arXiv:1203.3556] [INSPIRE].
J. Bhattacharya, S. Bhattacharyya, S. Minwalla and A. Yarom, A Theory of first order dissipative superfluid dynamics, JHEP 05 (2014) 147 [arXiv:1105.3733] [INSPIRE].
V. Bargmann, On Unitary ray representations of continuous groups, Ann. Math. 59 (1954) 1.
R. Andringa, E. Bergshoeff, S. Panda and M. de Roo, Newtonian Gravity and the Bargmann Algebra, Class. Quant. Grav. 28 (2011) 105011 [arXiv:1011.1145] [INSPIRE].
K. Jensen, Aspects of hot Galilean field theory, JHEP 04 (2015) 123 [arXiv:1411.7024] [INSPIRE].
K. Jensen and A. Karch, Revisiting non-relativistic limits, JHEP 04 (2015) 155 [arXiv:1412.2738] [INSPIRE].
M. Geracie, K. Prabhu and M.M. Roberts, Fields and fluids on curved non-relativistic spacetimes, JHEP 08 (2015) 042 [arXiv:1503.02680] [INSPIRE].
D.T. Son, Vanishing bulk viscosities and conformal invariance of unitary Fermi gas, Phys. Rev. Lett. 98 (2007) 020604 [cond-mat/0511721] [INSPIRE].
C. Hoyos, B.S. Kim and Y. Oz, Lifshitz Hydrodynamics, JHEP 11 (2013) 145 [arXiv:1304.7481] [INSPIRE].
C. Hoyos, B.S. Kim and Y. Oz, Lifshitz Field Theories at Non-Zero Temperature, Hydrodynamics and Gravity, JHEP 03 (2014) 029 [arXiv:1309.6794] [INSPIRE].
C. Hoyos, B.S. Kim and Y. Oz, Bulk Viscosity in Holographic Lifshitz Hydrodynamics, JHEP 03 (2014) 050 [arXiv:1312.6380] [INSPIRE].
C. Eling and Y. Oz, Hořava-Lifshitz Black Hole Hydrodynamics, JHEP 11 (2014) 067 [arXiv:1408.0268] [INSPIRE].
C. Hoyos, A. Meyer and Y. Oz, Parity Breaking Transport in Lifshitz Hydrodynamics, JHEP 09 (2015) 031 [arXiv:1505.03141] [INSPIRE].
M. Taylor, Lifshitz holography, Class. Quant. Grav. 33 (2016) 033001 [arXiv:1512.03554] [INSPIRE].
J. Hartong, N.A. Obers and M. Sanchioni, Lifshitz Hydrodynamics from Lifshitz Black Branes with Linear Momentum, JHEP 10 (2016) 120 [arXiv:1606.09543] [INSPIRE].
R.A. Davison, S.s. Grozdanov, S. Janiszewski and M. Kaminski, Momentum and charge transport in non-relativistic holographic fluids from Hořava gravity, JHEP 11 (2016) 170 [arXiv:1606.06747] [INSPIRE].
M. Garbiso and M. Kaminski, Dispersion relations in non-relativistic two-dimensional materials from quasinormal modes in Hořava Gravity, JHEP 10 (2019) 087 [arXiv:1905.11993] [INSPIRE].
D. Fernández, A. Rajagopal and L. Thorlacius, Non-equilibrium steady states in quantum critical systems with Lifshitz scaling, JHEP 12 (2019) 115 [arXiv:1909.06377] [INSPIRE].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 1911.02578
Rights and permissions
Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Novak, I., Sonner, J. & Withers, B. Hydrodynamics without boosts. J. High Energ. Phys. 2020, 165 (2020). https://doi.org/10.1007/JHEP07(2020)165
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP07(2020)165