Orientational order parameters for arbitrary quantum systems

TL;DR

This paper introduces a generalized framework for defining orientational order parameters in quantum systems using Wigner function expansions, applicable to diverse systems like Fermi liquids, spin, and molecular systems.

Contribution

It extends classical nematic order concepts to quantum mechanics, providing new order parameters for molecular systems beyond traditional tensor descriptions.

Findings

Unified quantum order parameter framework developed

Demonstrated on Fermi liquids and spin systems

Derived novel order parameters for complex molecular systems

Abstract

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.