Hartmut-Loewen.pdf

“adiabatic“ approximation: assume the pair correlations in
nonequilibrium are the same as those for an equilibrium system with
v
the same one-body density profile (established by a suitable V ˆ ext (r, ω,t))
v
∂ρ(
r,
ˆ ω,
t)
v t
v
⎡ v v δF
= ∇ v • D(
ˆ)
• ⎢ ( r,
ˆ
r ω ρ ω,
t)
∇ v
r
∂ t
⎢
⎣
δδρ
( r,
ˆ ω,
t )
v
⎡
[ ] ⎤
+ ˆ v ˆ δF
ρ(
r,
ˆ ω,
t)
D ⎢ ( , ˆ
r rR⎢
ρρ ( r,
ω , t ) R v ⎥⎦
⎣
δ ( ˆ )
⎥
⎣
δρ(
r,
ˆ ω,
t)
⎦
[ ρ(
r,
ˆ ω,
t)
] ⎤
v ⎥⎦
⎥
⎦
DDFT
with the equilibrium Helmholtz free energy density functional
v
v
3 v v
[ ( ) ] [ ] d r d ˆ ωρ(
r,
ˆ ω)
V ( r,
ˆ ω,
t)
3
3
[ ρ]
= k T d r d ˆ ( r,
ˆ ) ln ( r,
ˆ
B ∫ ∫ ωρ
ω Λ ρ ω)
− 1 + Fext
ρ + ∫
F ext
(M. Rex, H.H. Wensink, H.L., PRE 76, 021403 (2007))
∫