Cholesteric Helix and Tensor of Orientational Order

We can imagine a cholesteric as a smck of nematic quasi-layers of molecular thickness a with the director slightly turned by ( ) from one layer to the next one. In fact it is Oseen model [18]. Such a structure is, to some extent, similar to lamellar phase. Indeed, the quasi-nematic layers behave like smectic layers in formation of defects, in flow experiments, etc. Then, according to the Landau-Peierls theorem, the fluctuations of molecular positions in the direction of the helical axis blur the one-dimensional, long-range, positional (smectic A phase like) helical order but in reality the corresponding scale for this effect is astronomic. 

In the first approximation, the parameter of the local orientational order of a cholesteric liquid crystal is the same uniaxial traceless tensor Qij = S njnj — 5,y/3) as in the nematic phase with the director axis always lying in the x,y-plane, e.g. along the x directirMi at a selected cross-section of the helix  

In the helical structure this tensor, as well as the tensor of the dielectric anisotropy (ellipsoid) rotates upon the translation along the z-axis as shown in 

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