Quantum description of the orientational degrees of freedom in a biaxial nematic liquid

The quantum mechanical version of a classical model for studying the orientational degrees of freedom corresponding to a nematic liquid composed of biaxial molecules is presented. The effective degrees of freedom are described by operators carrying an SU(3) representation, which allows the explicit calculation of the partition function in the mean field approximation. The algebraic consistency conditions are solved numerically and the equilibrium phases of the system are determined. Phase diagrams corresponding to one extreme quantum case, together with the almost classical case are presented. The specific heat is also calculated for different choices of the constituent biaxial molecules. Our results reproduce the classical calculation in the limit of high temperatures and high quantum numbers. They present some interesting differences arising from the quantum behavior in the low-temperature limit.