Non-relativistic transport from frame-indifferent kinetic theory
arXiv:2407.08805 · doi:10.1103/fk7x-bkd9
Abstract
This paper explores the application of Newton-Cartan geometry to the kinetic theory of gases that includes non-relativistic gravitational effects and the principle of general covariance. Starting with an introduction to the basics of Newton-Cartan geometry, we examine the motion of point particles within this framework, leading to a detailed analysis of kinetic theory and the derivation of conservation equations. The equilibrium distribution function is explored, and the example of a rotating gas in a gravitational field is discussed. Further, we develop covariant hydrodynamic equations and extend our analysis through a gradient expansion approach to assess first-order constitutive relations for rotating gases. Finally, we address the frame-dependence paradox, presenting a novel resolution that addresses apparent discrepancies. Our construction resolves a fifty-year-old debate about the frame-indifferent formulation of kinetic theory. The resolution is presented in a modern, symmetry-based approach.
29 pages, 1 figure
References in corpus (29)
- Toward an AdS/cold atoms correspondence: a geometric realization of the Schroedinger symmetry
- On the coupling of Galilean-invariant field theories to curved spacetime
- Non-Relativistic Gravity and its Coupling to Matter
- Torsional Newton-Cartan gravity from the large expansion of General Relativity
- Observation of ultracold atomic bubbles in orbital microgravity
- Revisiting non-relativistic limits
- Anomalous bulk-edge correspondence in continuous media
- A short review on Noether's theorems, gauge symmetries and boundary terms
- A bulk-interface correspondence for equatorial waves
- Electrical conductivity of a warm neutron star crust in magnetic fields
- Aspects of hot Galilean field theory
- Vortex-antivortex physics in shell-shaped Bose-Einstein condensates
- Non-Abelian anomalies in multi-Weyl semimetals
- Transport coefficients of hot and dense hadron gas in a magnetic field: a relaxation time approach
- An introduction to the relativistic kinetic theory on curved spacetimes
- Topology in shallow-water waves: a violation of bulk-edge correspondence
- Superfluid vortex dynamics on a spherical film
- Superfluid vortex dynamics on an ellipsoid and other surfaces of revolution
- One particle distribution function and shear viscosity in magnetic field: a relaxation time approach
- Can material time derivative be objective?
- Null Fluids - A New Viewpoint of Galilean Fluids
- Non-relativistic Spinning Particle in a Newton-Cartan Background
- Gauge Invariance and Anomalies in Condensed Matter Physics
- Absolute Time Derivatives
- Hydrodynamics of Quantum Vortices on a Closed Surface
- From the Boltzmann equation to fluid mechanics on a manifold
- Effect of Coriolis force on the shear viscosity of quark matter: A nonrelativistic description
- Canonical Analysis of Non-Relativistic Particle and Superparticle
- Canonical Formulation of a New Action for a Non-relativistic Particle Coupled to Gravity