Weakly interacting homogeneous Bose gas: The role of residual interactions

Author(s): C. Weiss, S.-A. Biehs, A. Eckardt, M. Holthaus
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Article: Laser Physics
Keywords: weakly interacting bose gas, born approximation, s-wave scattering length, ground-state energy
PACS: 03.75.Hh, 67.40.Db, 05.30.Jp
Abstract:: The calculation of the ground-state energy of a homogeneous Bose gas with soft interparticle interaction results in an expression originally stated by Brueckner and Sawada, instead of the more accurate Lee-Yang formula. We show that the source of this discrepancy lies in the residual terms of the full Hamiltonian which are neglected in the standard Bogoliubov scheme. Incorporating these residual interactions, we derive an improved upper bound on the ground-state energy. An important link in our chain of arguments consists in the fact that the Born series of the scattering length is a convergent rather than an asymptotic expansion at least for su ciently soft potentials. We provide an exactly solvable model which demonstrates that the Born series of the scattering length reproduces, within its radius of convergence, the exact scattering length.
URL: http://www.physik.uni-oldenburg.de/condmat/Papers/p_lphys04.pdf (application/pdf)