[lammps-users] questions on summation of autocorrelation function

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1

I’d like to obtain thermal conductivity using Green-Kubo method.
I’ve run the NVT job using timestep 1 fs for 1000000 steps after equilibration.
During this running, I made output of heat flux every 10 steps.
Then, I obtain autocorrelation of heat flux and its summation using correlate.py, (e.g. correlate.py -c 6 -s 1000 flux.log flux.out).
I think the summation should converge even though I increase max correlation time (in above case, it is 1000) as much as possible (in principle, even infinite will be all right).

  1. It seems to converge around 1000~2000. However, it increases further and even decreases as max correlation time increases much.
    Is it common tendency?

Then, should I take some moderate value for max correlation time?
If so, what should it be? Is it 1000~2000?
Otherwise, what’s wrong with it and what should I do for it?

  1. If I take 1 fs as timestep, will it better to increase interval time for outout to 40~50 instead of 10?
    By the way I think multiplation of dt (time interval for output) is missing in final summation value of correlate.py.
    Is it right?

Best regards,

Luke

2

These are Green-Kubo questions more than LAMMPS questions. You can read ¡°Statistical Mechanics of NonEquilibrium Liquids¡± by Evans and Morriss online for free: http://rsc.anu.edu.au/~evans/evansmorrissbook.php Also note that ¡°At long times the flux at time t, J(t), is uncorrelated with its value a long time earlier J(0) and the autocorrelation function decays to zero.¡± (see: http://en.wikipedia.org/wiki/Green%E2%80%93Kubo_relations )

Regarding the correlate.py script and your second question, note the comment in the header of correlate.py:

¡°The total sum of the correlation is also computed which can be converted to an integral by multiplying by the timestep.¡±

Paul

3

I'll just add that you should search past messages on this mail list.
There has been a lot of discussion about using the GK method
and how to do it.

Steve