March 2013
Intermediate to advanced
406 pages
14h 48m
English
Content preview from Perturbation Theories for the Thermodynamic Properties of Fluids and Solids
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Free Energy Perturbation Theories for Simple Fluids and Solids 153
Inserting this result into Equation 6.91 leads to
Q
c
= Q
(
0
)
c
exp
−
1
2
βNρ
1 −N
−1
ˆu
1
(
0
)
k
exp
βρˆu
1
(
k
)
k
s
(
k
)
0
,
(6.93)
where
s
(
k
)
= exp
−
βˆu
1
(
k
)
V
ˆρ
(
k
)
ˆρ
(
−k
)
(6.94)
is the k
th
mode and ρ = N/V the number density. The simplest approximation to the
average in Equation 6.93 is the RPA
k
s
(
k
)
0
≈
k
s
(
k
)
0
, (6.95)
which would be exact if there were only one k vector in the half k-space. Successive
improvements can be obtained by replacing the average in Equation 6.93 with a
product involving averages over products of an increasing number of modes. This
is the essence of the mode expansion, ...
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