The name is absent

However, the quantity of interest is the ratio of the partition function of the chain in
the presence of an external field to the one in absence of it,

ʃ Drexp (-ffi∕₀[r] - ∕3f∕₁[r, w])
ʃ Drexp (—χ3C7₀[r])

This can be further approximated as

Q[w] ≈ — / ⅛^m-⁺¹ [exp(-Δsw(rjv_s))Φ(rjv_s - r_Ns-i) exp(-∆sw(r_jv_s-ι))

Φ(r₇v_s-ι - r₇v_s-₂)∙∙∙ exp(-Δsw(rι))Φ(rι - r₀) exp(-∆sw(r_o))].        (8.19)

Or,

Q[w] = — / dr g(r, N- [w]) = — / dr q(γ, N — s; [w])g(r, s; [w]),       (8.20)
where

q(r, 0; [w])       = exp(-∆sw(r))

(8.21)

q(r, s + ∆s; [w]) = exp(-∆sw(r)) ʃ dr'Φ(r — r^l)q(r^l, s; [w])

Physically, g(r, s; [w]) represents the statistical weight for a chain of length ‘s’ with its
end at position r. This is similar to the probability density, pŋ(r, s) in the absence of
the external field. Using this analogy, eqn. 8.21 is a Chapman-Kolmogorov equation
in the presence of an external field, and the resulting Fokker-Planck equation is given

214

<<   223   224   225   226   227   228   229   >>

More intriguing information