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. We generalize this method to quantum mechanics based on an expansion of Wigner functions. This provides a unified framework applicable to arbitrary quantum systems. The formalism is demonstrated for the cases of Fermi liquids and spin systems. Moreover, we derive new order parameters for molecular systems, which cannot be properly described with the usual nematic tensors.