content_image/348935.jpg content_image/348941.jpg
<img src='content_image/348935.jpg'>

where we find A = 31 . 80(15) and B = 144 . 20(3). The uncertainties were obtained, using error bars obtained from 16 independent runs of the program. We test other temperature values but we did not find difference as expected when E$_{F}$ is in the middle of band gap in this case where a uniform density of states is considered. 

Extending our results, we can compute the second moment: 

which yields 〈 n ( t ) $^{2}$〉 = N$_{tr}$ Pr( k | n (0) , t ) + N$_{tr}$ ( N$_{tr}$ − 1)Pr( k | n (0) , t ) 2 ≈ 〈 n ( t ) 〉 + 〈 n ( t ) 〉 2 

So we have 〈 n ( t ) $^{2}$〉 ≈ N$_{tr}$ ln − $^{1}$10 2( p$_{max}$ − p$_{min}$ ) ∫ 10 − p $^{max}$t 10 − p min t du ( e − $^{u$_{−}$}$1 ) u + ln − $^{2}$10 N 2 tr 4( p$_{max}$ − p$_{min}$ ) 2 [ ∫ 10 − p $^{max}$t 10 − p min t du ( e − $^{u$_{−}$}$1 ) u ] 2 , which leads to 

<img src='content_image/348941.jpg'>

