Poisson-bracket approach to the dynamics of nematic liquid crystals

Abstract

We use the general Poisson-bracket formalism for obtaining stochastic dynamical equations for slow macroscopic fields to derive the equations that govern the dynamics of nematic liquid crystals in both their nematic and isotropic phases. For uniaxial molecules, we calculate the Poisson bracket between the tensorial nematic order parameter Q and the momentum density g, as well as those between all pairs of conserved quantities. We show that the full nonlinear hydrodynamical equations for the nematic phase derived in this formalism are identical to the nonlinear Ericksen-Leslie equations. We also obtain the complete dynamical equations for the slow dynamics of the tensorial nematic order parameter Q valid both in the isotropic and the nematic phase. They differ from those obtained by other techniques only in the values of kinetic coefficients and in the number of nonlinear terms in Q, which are present.