Kinetic theories: from curved space to flat space

TL;DR

This paper extends the equivalence between off-equilibrium states and gravitational perturbations from macroscopic to microscopic particles, including vorticity effects, by mapping kinetic theories in curved space to flat space, predicting spin polarization phenomena.

Contribution

It generalizes the equivalence to include vorticity via torsional perturbations and applies it to kinetic theories of particles, predicting spin polarization in elastic materials and Dirac semi-metals.

Findings

Equivalence established for hydrodynamic and elastic regimes.

Spin polarization induced by shear strain variation predicted.

Order-of-magnitude estimate provided for Dirac semi-metal polarization.

Abstract

We generalize the equivalence between off-equilibrium state and gravitational perturbation of equilibrium state from dynamics of macroscopic quantities to that of microscopic particles. We also generalize the equivalence to incorporate off-equilibrium state with vorticity by torsional perturbation to equilibrium state. The equivalence is achieved by mapping kinetic theories of spinless and spinning particles in torsional curved space to flat space through suitable choice of inertial frame that eliminates geodesic forces on particles. The equivalence has been shown for hydrodynamic and elastic regimes. In the latter case, we predict spin polarization induced by time-variation of shear strain in elastic materials. We also provide an order-of-magnitude estimate for the polarization in Dirac semi-metal.