Orientational Order Parameters for Arbitrary Quantum Systems

The concept of quantum-mechanical nematic order, which is important in systems such as superconductors, is based on an analogy to classical liquid crystals, where order parameters are obtained through orientational expansions. This method is generalized to quantum mechanics based on an expansion of Wigner functions. This provides a unified framework applicable to arbitrary quantum systems. The formalism recovers the standard definitions for spin systems. For Fermi liquids, the formalism reveals the nonequivalence of various definitions of the order parameter used in the literature. Moreover, new order parameters for quantum molecular systems with low symmetry are derived, which cannot be properly described with the usual nematic tensors.