High-temperature chiral phases: a role of fluctuations

A connection between chirality at the molecular and mesoscopic scales and the corresponding macroscopic chiral structure of liquid crystalline phases is one of key issues of soft matter research. The most appropriate theoretical tools to study chirality-induced structures are statistical field theory of correlation functions and computer simulations. The correlations are calculated for the order parameter fields that enter phenomenological description of a given chiral phase, like two-point correlations for cholesterics as constructed out of the alignment tensor field. A quantity that could subsequently be derived from such correlations and used to measure chirality is, for example, the optical activity tensor or, as for bent-core systems, the traceless and symmetric third-rank tensor. In this paper we explicitly show a relation between chirality and two-point correlations of the alignment tensor field. The correlations are determined from Monte-Carlo simulations for a model isotropic liquid of chiral Gay-Berne fluid. The calculated molecular quantities are consistent with recent predictions of statistical field theory.