Info

where

is the functional with the value at n = 0 to be a distribution function averaged over a random field

It is assumed that summing over repeated indices is carried out in Eq. 2.2.10. A common method of solving the Eq. 2.2.10 is to represent the functionals Y[;r, p, t ] and Sln 0[n]/£na(r, t) as the functional power series r p, t ] = f (i% p, t) + \na (rb t1 )F1a (r, t; r1, t1; pH^

+ Ina(r1, t\Ylp(2, t2 )F2aj3(r, t;rb t^, t^; p )dr1dt1dr2dt2 + , (2.2.14)

+ J Ba/3y (r, t; rb t1; r2, t2 )(r1, t1 }]r (r2, t2 ))r1dt1dr2dt2 + ...,(2.2.15)

where F, Fa, F2ap are the functionals of the zero, the first and the second power, respectively; Bap is the correlation tensor of a random magnetic field of the second rank which is determined by the Eq. 2.2.9, and Ba^y is the correlation tensor of the third rank.

Substituting these expressions into Eq. 2.2.10 and equating the functionals of equal power on the left and right hand sides of Eq. 2.2.10, as a result we obtain an infinite set of related equations. The simplest method of solving of these equations is to equate one of the functionals Fn to zero. Let F2 = 0, then d- + L0 jF (r, p, t) = -iDaF1a(r, t;r, t; p )

d- + Lo j Fa (r, t; rb t1; p) = iBa^r, t; r1, t1 )DpF (r, p, t). (2.2.16)

To solve the set of Eq. 2.2.16 let us introduce the functions <pa(r, t;rb tb p) according to the relation

Fla(r, t;rl, t1; p)=exp(- Lot D'a(r, ^b t1; p). (2.2.17)

The action of the operator exp(- L0t) on an arbitrary function of the coordinates and moments is the replacement r by r -Ar(t) and p by p -Ap((), where Ar(t) and Ap(() is the variance of the radius-vector and the momentum of a particle in a regular field. Substituting the expression for F1a into the second equation of the set Eq. 2.2.16, we obtain

Fa(r, t;rb p) = -/J exp(- Lo (t - t'))Baj3(r, t';rb t1 ))F(r, p, t). (2.2.18)

Was this article helpful?

0 0

Post a comment