content_image/332037.jpg content_image/332033.jpg content_image/332036.jpg content_image/332035.jpg content_image/332030.jpg content_image/332029.jpg content_image/332032.jpg content_image/332031.jpg
small τ$_{0}$ (= large a/b ) we have [16] 

so that 

because α$_{m}$ = β$_{m}$ for large m . Here n is odd or even for the Ce or Se modes, respectively. We conclude therefore that 

has to be large and justify large q ∼ m $^{2}$. 

2. Evaluating the determinant 

Each mode contributes 

<img src='content_image/332037.jpg'>

<img src='content_image/332033.jpg'>

<img src='content_image/332036.jpg'>

<img src='content_image/332035.jpg'>

Since a is large, the sum over m can be replaced by an integral over ω = m/a like in Ref. [18] and for large q 1 / 2 ∼ m ∼ a/b , we have 

where 

so that 

For large r the integral on the right-hand side is proportional to r and we can get the coefficient of proportionality by differentiating with respect to r . This gives 

<img src='content_image/332030.jpg'>

<img src='content_image/332029.jpg'>

<img src='content_image/332032.jpg'>

<img src='content_image/332031.jpg'>

