derivation of kinetic equations from the generalized langevin equation
TRANSCRIPT
PHYSIC A L REVIEW A VOLUME 2, NUMBER 5 NOVEMBER 1970
1 k kZZ —v y—v v(r ) q dr"
2 m no m' n Pq 0
1 k 2 kZ Z —v„i y, i' —v„v(r„)dr"
21 p~~~
kp )
4 „,„, ' m
1, k - ' ¹(k)= —Ã' g(r) —v v(r) dr = (t&, V),
2 m 3m
where
(~V) =N f g(r)v v(r)dr
- means "when k is large enough to make S(k) equalto 1, " and we have done a. pa, rtial integration in the
fifth line and used the definition of the radial dis-tribution function g(r) is the sixth. Thus we find
(k~(H- Z, (k))'~k) - (~V)
instead of zero as concluded before. It follows di-rectly that
(kI H Ik) - E,'$)+4(K)c(k)E, (k)+ (b, V)e (k)
and that the validity of the Mihara-Puff conjecturehinges upon the smallness of the third term on theright-hand side in comparison with the first two
terms If w.e use Sear's recent estimate of (b, V)
[Phys. Rev. 185, 200 (1969)]we get 3(AV) =148'KA and find that, with (Z) = 14 'K, the third termis less than 5 of the right-hand side for k &3 A
Therefore, our conclusion, that the Mihara-Puffconjecture
(kIH'Ik) = &„'(k)+4(A)s(k)Z, (k)
is accurate for all k large enough to make S(k) equalto unity, would still seem to be valid, although itstruth is no longer axiomatic but asymptotic.
Derivation of kinetic Equations from the Genera)izedLangevin Equation. A. Z. Akcasu and J. J.Duderstadt [Phys. Rev. 188, 479 (1969)]. Severaltypographical errors occurred in this article:
(i) The symbol G is missing from the title ofSec. II, as well as in two places in Eq. (32).
(ii) A plus sign should appear between the inte-grals on the second line of Eq. (29).
(iii) Replace P by p' in Eq. (22) and G by G in
Eq. (41).(iv) In Eq. (35), define b(p) —= (1 —P,)i(p).
Propagation of Small-Area Pulses of Coherent Lightthrough a Resonant Medium. M. D. Crisp[Phys. Rev. A 1, 1604 (1970)]. (i) Equation (2a) on
page 1605 should read
(X Ic) -i&a(t c)s/c&ci-y(g, t& —2
(ii) Equation (26) on p. 1607 should read
g( ),g ((C —Ccic) C —c)c/c)'c'
T2 &0
&& U(t —&Is/c) Z~(2[v(os(t —&7@/c)]~t ~) .