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The autocorrelation function
introduced in the previous Section is here
the normalized VACF
 |
(4.71) |
hence
.
Here
is the x-, y-, or z-component of the velocity of a `tagged' atom.
The memory function
of
is defined by the relation
 |
(4.72) |
Eq. (4.72) is called the memory function equation.
Within the AR-model the z-transform of the VACF has the form
 |
(4.73) |
Here the
are the zeros of
 |
(4.74) |
We recall that the z-transform of an arbitrary discrete function
is given by
, and the inverse transform by
. Applying the inverse z-transform to (4.73) yields
 |
(4.75) |
where the coefficients
are given by
 |
(4.76) |
Note that
has a multiexponential form, and that the stability criterion
 |
(4.77) |
must be fulfilled. This is guaranteed by the Burg-algorithm [60,61].
Next: Density of states within
Up: Theory and implementation
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pellegrini eric
2009-10-06