Orientational order parameters for arbitrary quantum systems

The concept of orientational order is of central importance for both classical liquid crystals and quantum-mechanical systems such as superconductors. In classical systems, order parameters can be obtained through systematic orientational expansions [1]. We generalize this method to quantum mechanics based on an expansion of Wigner functions. This provides a unified framework applicable to arbitrary quantum systems [2]. 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.

[1] M. te Vrugt and R. Wittkowski, AIP Advances 10, 035106 (2020)
[2] M. te Vrugt and R. Wittkowski, Annalen der Physik, 2000266 (2020)