NoséHoover method
[W. Hoower, Phys.Rev.A 31, 1695 (1985)]
I
The Hamiltonian is modified by adding a virtual degree of
freedom (timescale variable
s
) with its own
K
s
and
U
s
.
I
This introduces a dimensionless friction factor with virtual
mass
Q
, which controls the rate of change in
T
.
I
The Hamiltonian and equations of motion become
H
=
X
i
p
i
2
m
i
+
U
(
q
i
) +
p
2
s
2
Q
+
gk
B
T
ln
(
s
)
(30)
d
q
i
d
t
=
p
i
m
1
;
d
p
i
d
t
= 
d
V
d
q
i

p
s
p
i
;
d
p
s
d
t
=
∑
i
p
i
m
i

gk
B
T
Q
.
(31)
I
Modified equations of motion guarantee that the original
degrees of freedom follow properly the isotherm.
I
Nosé suggested
Q
≈
gk
B
T
(
g
is the number of degrees of
freedom in the system).
Notes
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NoséHoover Chain Method
[Tobias et al., J.Phys.Chem. 97, 12959 (1993)]
I
A chain is formed of the parameters
s
so that one always
controls the previous one.
I
This is needed for some cases to avoid ergodicity
problems with the standard NoséHoover method.
I
In the
Massive NoséHoover chain
method, a thermostat
is connected to
every
degree of freedom.
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 Winter '12
 Kotakoski
 Trigraph, noséhoover chain method

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