Shumway Research Group

Department of PhysicsArizona State UniversityTempe • AZ
Research in Path Integral Simulations, Quantum States of Matter, and Nanoscale Electronics

Path Integral Simulation of Bose Condensation

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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.)

NSF logo 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.