We study the effects of repulsive interaction and disorder on bosons in a two-site Bose–Hubbard system, which provides a simple model of the dirty boson problem . By comparison with exact numerical results, we demonstrate how a straightforward application of the Bogoliubov approximation fails even to deliver a qualitatively correct picture. It wrongly predicts an increase of the condensate depletion due to disorder. We show that, in the presence of disorder, the noncommutative character of the condensate operator has to be retained for a correct description of the system. While these corrections to a simple meanfield Bogoliubov theory are usually small in extended systems, we show that care has to be taken when modeling small inhomogeneous Bose systems.We study the effects of repulsive interaction and disorder on bosons in a two-site Bose–Hubbard system, which provides a simple model of the dirty boson problem . By comparison with exact numerical results, we demonstrate how a straightforward application of the Bogoliubov approximation fails even to deliver a qualitatively correct picture. It wrongly predicts an increase of the condensate depletion due to disorder. We show that, in the presence of disorder, the noncommutative character of the condensate operator has to be retained for a correct description of the system. While these corrections to a simple meanfield Bogoliubov theory are usually small in extended systems, we show that care has to be taken when modeling small inhomogeneous Bose systems.

arXiv:1305.4120Journal of Physics A Mathematical and TheoreticalDec 16, 20132 citations

Bogoliubov theory on the disordered lattice

Christopher Gaul, Cord Axel Müller

arXiv:1209.5446The European Physical Journal Special TopicsFeb 1, 201317 citations

Bose-Einstein condensation in a minimal inhomogeneous system

Christopher Gaul, Jürgen Schiefele

We study the effects of repulsive interaction and disorder on bosons in a two-site Bose–Hubbard system, which provides a simple model of the dirty boson problem. By comparison with exact numerical results, we demonstrate how a straightforward application of the Bogoliubov approximation fails even to deliver a qualitatively correct picture. It wrongly predicts an increase of the condensate depletion due to disorder. We show that, in the presence of disorder, the noncommutative character of the condensate operator has to be retained for a correct description of the system. While these corrections to a simple meanfield Bogoliubov theory are usually small in extended systems, we show that care has to be taken when modeling small inhomogeneous Bose systems.We study the effects of repulsive interaction and disorder on bosons in a two-site Bose–Hubbard system, which provides a simple model of the dirty boson problem. By comparison with exact numerical results, we demonstrate how a straightforward application of the Bogoliubov approximation fails even to deliver a qualitatively correct picture. It wrongly predicts an increase of the condensate depletion due to disorder. We show that, in the presence of disorder, the noncommutative character of the condensate operator has to be retained for a correct description of the system. While these corrections to a simple meanfield Bogoliubov theory are usually small in extended systems, we show that care has to be taken when modeling small inhomogeneous Bose systems.

Jan 17, 20142 citations

REMARKS ON THE BOGOLYUBOV MODEL FOR BOSONS AND SIMILAR MODELS.

Nicolaas Marinus Hugenholtz

Jan 1, 19690 citations

Disordered bosons: Condensate and excitations

Kanwal G. Singh, Daniel S. Rokhsar

The disordered Bose-Hubbard model is studied numerically within the Bogoliubov approximation. First, the spatially varying condensate wave function in the presence of disorder is found by solving a nonlinear Schr\"odinger equation. Using the Bogoliubov approximation to find the excitations above this condensate, we calculate the condensate fraction, superfluid density, and density of states for a two-dimensional disordered system. These results are compared with experiments done with $^{4}\mathrm{He}$ adsorbed in porous media.The disordered Bose-Hubbard model is studied numerically within the Bogoliubov approximation. First, the spatially varying condensate wave function in the presence of disorder is found by solving a nonlinear Schr\"odinger equation. Using the Bogoliubov approximation to find the excitations above this condensate, we calculate the condensate fraction, superfluid density, and density of states for a two-dimensional disordered system. These results are compared with experiments done with $^{4}\mathrm{He}$ adsorbed in porous media.

arXiv:cond-mat/9307039Physical review. B, Condensed matterApr 1, 199449 citations

^{4}\mathrm{He}

adsorbed in porous media.