Deviations from Linear Theory for Fluctuations below the Supercritical Primary Bifurcation to Electroconvection

Abstract

Over two decades ago it was predicted that nonlinear interactions between thermally driven fluctuations in dissipative nonlinear nonequilibrium systems lead to deviations from mean-field theory. Here we report experimental observations of such deviations as a supercritical primary bifurcation is approached. We measured the mean-square director-angle fluctuations $〈{\ensuremath{\theta}}^{2}〉$ below the bifurcation to electroconvection of two different nematic liquid crystals. For ${\ensuremath{\epsilon}}_{\mathrm{mf}}\ensuremath{\equiv}{V}^{2}/{V}_{\mathrm{c},\mathrm{m}\mathrm{f}}^{2}\ensuremath{-}1\ensuremath{\lesssim}\ensuremath{-}0.1$ ( $V$ is the applied voltage) we find $〈{\ensuremath{\theta}}^{2}〉\ensuremath{\propto}|{\ensuremath{\epsilon}}_{\mathrm{mf}}{|}^{\ensuremath{-}\ensuremath{\gamma}}$ with $\ensuremath{\gamma}$ given by linear theory (LT). Closer to the bifurcation there are deviations from LT with a smaller $\ensuremath{\gamma}$ and with ${V}_{c}^{2}>{V}_{\mathrm{c},\mathrm{m}\mathrm{f}}^{2}$.