Conservative Brownian motion simulation of a hard-boson gas
Expositor: Dr. Wolfgang Paul – Institut für Physik, Martin Luther Universität, Halle (Saale), Alemania.
Fecha: Martes 23/02/2016 – 10.30 hs.
We present a simulation study of the properties of the Tonks-Girardeau gas, a system of N hard-core bosons confined in a one-dimensional harmonic trap. For this system the ground-state wave function is exactly known based on a Bose-Fermi mapping theorem. We employ Nelsons’ interpretation of quantum mechanics in which this N-body wave function gives rise to a set of stochastic differential equations for the positions of the N particles, which can be simulated by standard methods. Particularly, real space densities and momentum distributions can simply be determined by time averages along particle trajectories. Employing this approach we are able to significantly extend the range of particle numbers N treated numerically compared to earlier approaches, while reproducing all exactly known results for this model. We also show that for the bosons in a harmonic trap, contrary to what has been assumed so far, the momentum distribution reflects the system size scaling of the occupation numbers of the natural orbitals, i.e., it can be used to decide on the presence of a Bose-Einstein condensate.
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