Page 8 ... 2. 2. 0. 0. 1. ( ). (. ) 2 t t. Q t. M dudv. u v. M du t u u κ κ. = - = -. â«. â«. ,. (39). (. ) 2. 0. 0. (, , ) .... Academician of RAS K.M. Salikhov (KFTI RAS, Kazan).
http://mr-kzn.ru/proceedings/mrschool2016.pdf
LECTURE NOTES f
Z14 ³ dtdsdu S1 (t , s, u ) S0 (t ) S0 (u ) .
R1
(37)
0
Direct calculation produces () 1
R1
() 1
(r) 1
R ,
R
Q(t )
R
Z14 4
³
f
0
dtdsdue Q (t ) Q ( u ) e r < ( t , s , u ) 1 ,
t 1 M 2 ³ dudv N u v 0 2
M 2 ³ du (t u )N u , t
0
M 2 ³ dt '³ du 'N t ' s u ' .
< (t , s, u )
t
u
0
0
(38) (39) (40)
For preliminary qualitative understanding we should recognize, that essential range on t and u of the integrand is of order T2, while its duration on s has the order W c , because with increasing of s we have S1 (t , s o f, u ) o S0 (t ) S0 (u ) (or < (t , s o f, u ) o 0 ) that produces a rough estimation R1 Z14T22W c . If W c T2 , then this estimation is sufficient, but opposite relation W c T2 M 21/2 requires more refined analysis. Below, following to Refs. [5] and [3], we apply rather general form of the local field correlation function 32
N t
§ T W · 2T 0 ¨ ¸ . ¨ t2 T 2 W ¸ 2T 0 ¹ ©
(41)
This relation incorporates all existing qualitative information about correlations of dipole local fields on impurity nuclei taking into account existence of smooth quadratic in time evolution at t T2T , its transformation into linear in time dependence at T2T t W 0 with consequent transformation to 3d-diffusional asymptotics N (t ) t 3/2 at t W 0 . It is evident, that W c T2T W 0 here. It will be evident from the calculations that largest value has the term R1( ) from (38). It can be rewritten as R1( )
4 ³
Z14
T2 T
0
f
ds ³ ds T2 T
³ dtdu e f
0
Q ( t ) Q ( u )
e
< (t ,s , u )
1
R1( ) R1(! ) .
(42)
Looking for orders of values we can approximate R1( ) and R1(! ) as R1( ) () 1!
R
Z14
Z14
4 4
³
T2 T
³
f
0
T2 T
ds ³ dtdu e Q (t ) Q (u ) e ” and “
