##DSF lifetimes
Here are lifetimes predicted using the FWHM, \Gamma = 1/2\tau, of the spectral peaks of the DSF, Eq. (4):
https://github.com/jasonlarkin/disorder/blob/master/paper/vc/prb_vc_jl_112612.pdf
(note, click "View Raw")
The DSF was computed only along [100], [110], [111] directions.
\delta\omega_{i,i+1} is the level spacing when all modes are sorted in ascending order.
\deltaw_avg = average level spacing.
b=2 corresponds to a broadening of 2*\deltaw_avg.
there is a strong dependance of low-frequency modes for low c on the broadening b. this is because \delta\omega_{i,i+1} is much larger than \deltaw_avg at low frequency. this is a finite size effect.
However, for high-frequency modes at all c, the lifetimes are rather insensitive to b. In particular, the prediction from VC-NMD that the phonon lifetimes are consdierably larger than the Ioffe-Regel limit for c=0.05,0.15, is supported by this result. For c=0.5, all DSF lifetimes are less sensitive to b.
c=0.05
c=0.15
c=0.5
##method
https://github.com/ntpl/ntpl/wiki/Methods-Dynamic-Structure-Factor
##code
https://raw.github.com/jasonlarkin/disorder/master/matlab/m_dsf_long.m
#mode-by-mode for alloy c=0.5
#amorphous dispersion?
choosing max(S(k)) for k in the [100] direction, up to k = [pi/a 0 0] where a=lattice constant of the LJ crystal conventional cubic unit cell. So, for the following systems: 4x, 8x, 10x have box lengths of L = 4a, 8a, 10*a:
4x
8x
10x
