# Path Integral Simulation of Bose Condensation

This is a path integral Monte Carlo simulation of 16 bosons with mass m=1 in a 10x10x10 box. Every 2 seconds the screen updates with a snapshot of the configuration (there are thousands of Monte Carlo steps executed between frames). The boxes show the energy per particle and superfluid density. Data is collected for 4 second intervals, so there are noticible statistical fluctuations in the numerical values.

Adjust the slider to high temperature and note that the energy is about
3/2 kT. The size of the paths is the thermal deBroglie wavelength, proportional
to t^{-1/2}. At lower temperatures Bose statist ics become important.
See how the particles permute: small loops combine to form long chain.
The presence of macroscopic chains (here: paths that wind a cross the
simuation) is the signature of superfluidity.

The dashed box denotes the simulation cell, and the region outside the dashed box is just a periodic repetition. Dots on the paths indicate the zero slice of imaginary time.

(javadoc pages, download source.)

*This material is based upon work supported by the National Science
Foundation under Grant No. DMR 02-39819. Any opinions, findings, and conclusions
or recommendations expressed in this material are those of the author(s)
and do not necessarily reflect the views of the National Science Foundation.*