Spin Current in Hydrodynamics

Abstract

Hydrodynamic description of the spin degree of freedom has been drawing an increasing amount of attention in recent years. The reason for that attention lies in its diverse range of applications from condensed matter physics to astrophysics and high energy physics. After a brief discussion of the recent developments in hydrodynamics, we investigate relativistic hydrodynamics in the presence of a spin current. We generalize the results in the literature to describe a 2+1D fluid that is constrained only by Lorentz symmetry. We build the hydrodynamic equations for the energy-momentum tensor and the spin current. Then, we carry out an exhaustive analysis to identify constitutive relations, transport coefficients, and entropy. This setup enables us to solve hydrodynamic equations up to second order in gradients, i.e., in a Navier-Stokes level of approximation. Our framework reproduces well-known phenomena in the literature such as the spin Seebeck effect, thermal vorticity, Benett effect, and spin hydrodynamic generation. We further characterize more than 20 novel transport coefficients.