Dynamics of a trapped 1D Bose gas for finite interaction strength

We investigate the dynamics of a 1D Bose gas in a harmonic trap with point like interactions, recently studied experimentally in [1]. Starting from a discretisation of this model we calculate the groundstate properties and time evolution in the resulting Bose-Hubbard model using the time-evolving block decimation algorithm, TEBD. Both the case of vanishing interaction strength corresponding to the trivial case of free bosons, and the quasi integrable hard core case are well understood [2]. Furthermore recently exact solutions have been found in the absence of a trap potential and few particles [3]. We are focusing on the dynamics in the region with finite repulsive interaction and in a trap. Forall cases, using TEBD, we are able to calculate the propagation in both momentum and real space. \newline \newline [1] T. Kinoshita, T. Wenger, D. Weiss, Nature 440, 900 (2006) \newline [2] M. Rigol, V. Dunjko, V. Yurovsky, M. Olshanii, Phys. Rev. Lett. 98, 050405 (2007) \newline [3] H. Buljan, R. Pezer and T. Gasenzer, arXiv:0709.1444 (2007)