Wigner function approach to polarization-vorticity coupling and hydrodynamics with spin
Newly introduced equilibrium Wigner functions for particles with spin one-half are used in the semi-classical kinetic equations to study a possible relation between thermal vorticity and spin polarization. It is shown that in global equilibrium both the thermal-vorticity and spin polarization tensors are constant but not necessarily equal. In the case of local equilibrium, we define a procedure leading to hydrodynamic equations with spin. We introduce such equations for the de~Groot, van~Leeuwen, and van~Weert (GLW) formalism as well as for the canonical scheme (these two frameworks differ by the definitions of the energy-momentum and spin tensors). It is found that the GLW and canonical versions are connected by a pseudo-gauge transformation.
This paper presents derivation of the probability distribution for the area enclosed by a polymer loop in a gel and under different external fields using white noise analysis. In this context, the polymer loop is represented by Brownian paths and its immersion in a gel constraints it to occupy a constant area[1]. The external fields considered are electric field, and crossed electric-magnetic fields.