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Q: Quantenoptik

Q 311: Bose-Einstein Kondensation I

Q 311.8: Talk

Wednesday, March 6, 2002, 15:45–16:00, HS 22/B01

Path Integral Molecular Dynamics with Bosonic Exchange — •Harald Forbert and Dominik Marx — Theoretische Chemie, Ruhr-Universität Bochum, 44780 Bochum

One is often interested in the properties of many-body quantum systems. A well known method for investigating such systems is the Path Integral Molecular Dynamics (PIMD) method. In Bose-Einstein Condensates exchange statistics is crucial but usual PIMD algorithms can only handle the Boltzmann statistics of distinguishable particles. The approach to include the exchange in an exact exchange-potential thus far was limited to few particles only, since the calculation cost of the needed exchange term, a sum over all permutations, grows exponentially with the number of identical particles (“NP-hard”). Various approximations exist, but there is no control over the quality of these approximations. As a first step, we developed a new method of calculating the permanent of a positive matrix (the heart of the exchange potential) approximately to a predefined accuracy. We tested our approach by simulating 40 non-interacting particles in a harmonic oscillator potential at various temperatures and compared to exact analytical results.