Uniaxial nematic order (source code)

= Uniaxial nematic order
{title2=$Q_{ij}=\tfrac32\lambda(n_i n_j-\delta_{ij}/3)$}

A uniaxial <nematic order parameter> has one distinguished <nematic director> and equal <eigenvalues> in its perpendicular plane. In the displayed normalization the <eigenvalues> are $\lambda,-\lambda/2,-\lambda/2$, giving $\operatorname{Tr}Q^2=3\lambda^2/2$ and $\operatorname{Tr}Q^3=3\lambda^3/4$. Positive and negative $\lambda$ describe prolate and oblate orientational anisotropy, respectively; reversing the <nematic director> leaves the tensor unchanged.