München 2004 – scientific programme

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Q: Quantenoptik und Photonik

Q 18: Quantengase II

Q 18.5: Talk

Tuesday, March 23, 2004, 12:00–12:15, HS 225

Stochastic simulation of a one-dimensional Bose-gas via factorization of the kinetic energy — •Bernd Schmidt, Lev I. Plimak, and Michael Fleischhauer — Fachbereich Physik, Technische Univ. Kaiserslautern

The one-dimensional (1D) δ-interacting Bose-gas is a well suited model to test the feasibility of numerical methods for a later extension to simulating Bose-gases in general. Exact solutions are known for the homogeneous interacting gas [1] and predictions for the correlation properties can be derived by Bogolubov approximations [2,3].

We present an ab initio numerical method for calculating thermal properties of a 1D δ-interacting Bose-gas in a trap. Discretizing the system results in a Bose-Hubbard-like Hamiltonian. The imaginary time evolution of this Hamiltonian is made computationally accessible by stochastically factorizing the kinetic energy.

Applying ideas from density-matrix-renormalization-group techniques to the inhomogenous case allows us to enhance our calculations at low temperatures. We compare our numerical results to analytic predictions, covering the whole range from the Gross-Pitaevskii to the Tonks-Girardeau regime.

[1] E. H. Lieb and W. Liniger, Phys. Rev. 130, 1605 (1963).

[2] D. S. Petrov, G. V. Shlyapnikov, and J. T. M. Walraven, Phys. Rev Lett. 85, 3745 (2000).

[3] M. Olshanii and V. Dunjko, Phys. Rev. Lett. 91 (2003).