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.
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.