Long Range Correlations in Kinetic Theory

Cover Long Range Correlations in Kinetic Theory
Long Range Correlations in Kinetic Theory
Chelluri C a Sastri
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. And G. . Are the accelerations of the i-th particle due to external forces. ¥e assume that F^, =F, i(P. ), G.. =G^^(P, ) (2-3) and F. J. =F^2(Pi'Po), ^IJ =^12(Pi'^j) • We consider two cases; an integral e can be of type (a) : N e = XZ ^i ' e. = e-, (P. ) i=l ^ ^ ^ ^ or type (b) : N N e = Z: ^i +IZ^ B. J. , e. = e^(P. ), and e.^ = e^^iF^, I>. ) i * (x. ).
^ ^1 i=l ^ ^ Its expected value is = g^/f*l(x, )dP = N/^ fl(Pl)dPi X- eD, Hence, the number density v in 3-space is N/f -^ — . The number of
... pairs of molecules such that one is in D, and the other is in Dp is JZ a, eqn. (6-2) becomes - (''-2)[(''i3-^+V357'^2-^(''23-^-^°23-bJ)4] = ° (6-3) The set over which the assumption that |xp -x. , | ■> o fails is a strip of width 2a in six-dimensional space. But a is a small parameter, and ultimately v/e will take a limit in which -* 0. It can be shown by considering the initial value problem that if the terms dropped are small initially, they will remain small over a finite, macroscopic amount of time.

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