Hydrodynamics without boosts
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Springer
Received: January 29, 2020 Accepted: June 24, 2020 Published: July 23, 2020
Igor Novak,a Julian Sonnera and Benjamin Withersa,b a
Department of Theoretical Physics, University of Geneva, 24 quai Ernest-Ansermet, 1211 Gen`eve 4, Switzerland b Mathematical Sciences and STAG Research Centre, University of Southampton, Highfield, Southampton SO17 1BJ, U.K.
E-mail: [email protected], [email protected], [email protected] 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. Keywords: Global Symmetries, Holography and condensed matter physics (AdS/CMT), Space-Time Symmetries ArXiv ePrint: 1911.02578
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP07(2020)165
JHEP07(2020)165
Hydrodynamics without boosts
Contents 1 Introduction
1 3 4 4 5 5 6 9 12 14 15
3 Special cases 3.1 Lorentz boosts 3.1.1 Ideal hydrodynamic order 3.1.2 First order 3.1.3 Entropy current 3.2 Galilean boosts 3.3 Lifshitz scale invariance
16 16 17 18 19 19 21
4 Discussion
22
1
Introduction
Any system that finds itself in a state of local thermodynamic equilibrium, is thought to evolve to its global equilibrium state, described by universal long-wavelength, long timescale hydrodynamics, respecting positivity of entropy production. The universal theory governing this dynamics, corresponds to the relaxation of all conserved quantities of a given system, and can be adapted to particular physical situations of interest by specifying an equation of state, as well as the functional form and value in equilibrium of a specified set of transport coefficients [1]. Hydrodynamics is an extremely successful practical example of the philosophy of effective field theory. Its equations are formulated by arranging terms in ascending order of derivatives, truncating at a specified order in this expansion. 1 The possible terms that may appear in this expansion are restricted by the symmetries as well as the usual rules of effective field theories, in such a way as to reduce an a-priori redundant set of transport 1
For a clear review of this procedure in a relativistic system, see [2].
–1–
JHEP07(2020)165
2 Non-boost-invariant hydrodynamics 2.1 The ideal fluid 2.2 Dissipative corrections 2.2.1 Field redefinitions 2.2.2 Tensor structures and equations of motion ambiguity 2.2.3 First-order constitutive relations and
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