content_image/366381.jpg content_image/366383.jpg content_image/366385.jpg content_image/366387.jpg content_image/366389.jpg content_image/366391.jpg content_image/366393.jpg
Finally, with the help of the mappings (3.4), we can recognize the appropriate terms in the last equation, so that their ensemble average gives 

<img src='content_image/366381.jpg'>

The Poisson operator element L (2) l g ( r$_{1}$ , r$_{2}$ ) is obtained under similar approximations as above, but also the following approximations 

<img src='content_image/366383.jpg'>

which holds under the assumption of the difference in length scales (3.2), and the assumption 

<img src='content_image/366385.jpg'>

for n = ± 1. For the element L (2) l g ( r$_{1}$ , r$_{2}$ ), we then obtain 

<img src='content_image/366387.jpg'>

In order to express the previous equation in terms of the coarse-grained Doi-Ohta variables { P, p , l } , we must use the following closure approximation for the first term on the right hand side 

<img src='content_image/366389.jpg'>

where C is chosen in such a way that the previous expression is valid when its trace is taken. By putting α = β into the above equation, we find 

Using the above expressions, element L (2) l g ( r$_{1}$ , r$_{2}$ ) takes the final form 

<img src='content_image/366391.jpg'>

<img src='content_image/366393.jpg'>

