Hydrodynamics without boosts

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 R t ×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.

First order non-Lorentzian fluids, entropy production, and linear instabilities

“…Furthermore, Ref. [58] also extend the constitutive relations for such fluid, from the case where fluid is at rest (discussed in Sec. III C 3), to the case where it attains finite velocity.…”

“…Note added.-The work of [58], appeared in parallel, also discussed frame choices of the fluid without boost which overlap with Sec. III C 3 and Appendix of our manuscript.…”

Effective field theory for hydrodynamics without boosts

“…A linearised analysis of fluctuating isotropic and homogeneous configurations in charged hydrodynamics without boosts was done in [28]. A classification of first order transport in flat spacetime with the additional U(1) current was undertaken in [29], but a complete analysis of the second law constraints was not carried out. In this work, we develop further all of these lines of research by providing a complete covariant treatment and classification of transport in hydrodynamics without boosts within a field theoretic framework, including the presence of a U(1) current, and consider the most general fluctuation analysis around equilibrium states that are inherently anisotropic.…”

Newton-Cartan submanifolds and fluid membranes

“…In this work we considered Newton-Cartan geometry but there are many other types of non-Lorentzian geometries depending on the space-time symmetry group, which can be, e.g., Lifshitz, Schrödinger, or Aristotelian, which have direct applications for the hydrodynamics of strongly correlated electron systems as well as for the hydrodynamics of flocking behavior and active matter [37][38][39]90]. In these contexts, it is required to develop the mathematical description of submanifolds within these different types of ambient spacetimes.…”

“…1 As a nondynamical geometry its importance stems from the fact that it is the natural background geometry that nonrelativistic field theories couple to [25,26] 2 and thus provides a geometric and covariant formulation of many aspects of nonrelativistic physics including broad classes of long-wavelength effective theories such as hydrodynamics. In particular, in the past few years NC geometry and variants have been applied to the formulation of Galilean-invariant fluid dynamics [33,34], Lifshitz fluid dynamics [35,36] as well as hydrodynamics without boost symmetry [37][38][39][40], 3 which encapsulate the former as cases with extra symmetries. Furthermore, in the context of condensed matter systems, it was realized that NC geometry is the natural setting for developing an effective theory of the fractional quantum Hall effect [41][42][43][44].…”