Correlation functions and long-range order for a nematic in nonequilibrium stationary states - H. Híjar (Revista Mexicana de Física, 2006)
A thermotropic nematic thin film under the action of an external thermal gradient is studied theoretically. We use a fluctuating hydrodynamic approach and a time-scale perturbation formalism to calculate the orientation, temperature and velocity autocorrelation functions as well as the temperature-velocity fluctuations cross correlation function of the liquid crystal in the nonequilibrium state induced by the stationary heat flux. This method allows us to find, on slow time-scales, a contracted description in terms of the slow variables only, with a reduced dynamic matrix which can be constructed by the perturbation procedure. The wave number and frequency dependence of these correlation functions is evaluated analytically and their explicit functional form in the configuration space is also calculated for both equilibrium and steady states of the fluid. We show that, out of equilibrium, all these correlactions are long-ranged. We calculate the effects of this long-range behavior on the light scattering structure factor. Our results also show that the temperature and velocity autocorrelations contain two contributions, namely, a local equilibrium and a mode coupling contribution. From our quantitative estimations of these correlations, it can be established that the contribution due to the mode coupling mechanism is dominant over that based on spatial inhomogeneities in the fluctuation-dissipation relation.