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

TL;DR

This paper develops a quantum mechanical model for biaxial nematic liquid crystals using SU(3) operators, enabling calculation of thermodynamic properties and phase behavior, and reproduces classical results at high temperatures.

Contribution

It introduces a quantum SU(3) operator framework for biaxial nematic liquids, allowing explicit partition function calculation and phase analysis beyond classical models.

Findings

Reproduces classical results at high temperatures and quantum numbers

Calculates entropy, specific heat, and order parameters for various molecules

Determines equilibrium phases through numerical solutions

Abstract

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. In particular, the entropy, the specific heat and the order parameters are presented for different choices of the constituent biaxial molecules. Our results reproduce the classical calculation in the limit of high temperatures and high quantum numbers.