Recover quantum dynamics form PIGLET trajectory

[Anna ZHANG]

Hi everyone,

    I'm Anna. 

    I'm very interested in Michele's new arxiv paper "Inexpensive modelling of quantum dynamics using path integral generalized Langevin equation thermostats". It says that quantum dynamics can be recovered for PIGLET trajectory by deconvolution.  It also says that "The implementation of the method is made available as a post-processing tool of the opensource simulation code i-PI."

    But I did not find any post-processing tool for the deconvolution. Does anyone knows that where can I find it.

Thanks in advance!

ANNA

[venkat kapil]

Thanks for your interest. To compute the autocorrelation function you can run a simulation with i-PI say examples/tools/getacf/ and use ~/source/i-pi/bin/i-pi-getacf. It takes in units in atomic units (a.u.) only and returns in a.u as well. You can then follow the example examples/tools/gleacf/ to perform the deconvolution using ~/source/i-pi/bin/i-pi-gleacf. There is a README which describes how to use ~/source/i-pi/bin/i-pi-gleacf. If you want to use the PILGET thermostat, then make sure that you print out the centroid velocity. Use ~/source/i-pi/bin/i-pi-getacf to compute the velocity autocorrelation and then use ~/source/i-pi/bin/i-pi-gleacf to perform the deconvolution. Let me know if you have any problems.

[Anna ZHANG]

Dear Venkat,

    Thank you so much for your kind help! 

    I will try it!

Best Wishes

ANNA

[Anna ZHANG]

Dear Venkat,

I tried the example in example/tools/gleacf/h2o_gle, and I have a question regarding the parameter -dp xxx, i.e. the number of the iteration in the deconvolution process. 

When I use different iteration numbers, I get different results as shown in the attached picture. How can I know which -dp parameter is appropriate, and will the choose of different parameters induce artificial factors to the final results?

Best Wishes!

Anna Zhang 

[venkat kapil]

Exemplary parameters that you would use to compute the acf would be

i-pi-getacf -ifile simulation.vc.xyz -mlag 3072 -ftpad 1024 -ftwin cosine-hanning -dt '0.25 femtosecond' -oprefix vv

which would create the file "vv_facf.data". Note that the output will be in a.u. To perform the deconvolution I would use

i-pi-gleacf -a deconv -ifacf vv_facf.data -ixml input.xml -dp 1000, 50 -op deconv

which will produce files deconv_*. If you look at the header of one of these files, you will see that it the error and the laplacian is printed at each step. You can extract these diagnostics using : grep "#" deconv_* | awk '{print $6, $7}' > log
The optimal step number can be found by plotting
gnuplot> p "log" us 1:2:0 w labels
which should on a log-log plot should give you an "L-curve". Looking for the step number with the maximum curvature.
In the example (attached), the optimal point is close to 16 but since I am printing every 10 steps, it should correspond to the 160th file.
This approach is completely data driven and hence avoids bias. Let me know if you have further questions.

[Anna ZHANG]

Dear Venkat,

Oh, I see. Thank you so much for your detailed description!!!

Best Wishes!

Anna Zhang