https://doi.org/10.1140/epjst/e2013-01759-5
Regular Article
Condensation of interacting bosons in a random potential
1 Department of Mathematics and Statistics, McGill University, 805 Sherbrooke Street West, Montreal, QC H3A 2K6, Canada
2 Fakultät für Physik, Universität Wien, Boltzmanngasse 5, 1090 Vienna, Austria
3 Département de Mathématiques, Université d'Aix-Marseille (AMU) and Centre de Physique Théorique – UMR 7332, Luminy Case 907, 13288 Marseille Cedex 09, France
a e-mail: jakob.yngvason@univie.ac.at
Received:
9
September
2012
Revised:
15
January
2013
Published online:
11
March
2013
We study the effects of random scatterers on the ground state of the one-dimensional Lieb-Liniger model of interacting bosons on the unit interval. We prove that, in the Gross-Pitaevskii limit, Bose Einstein condensation takes place in the whole parameter range considered. The character of the wave function of the condensate, however, depends in an essential way on the interplay between randomness and the strength of the two-body interaction. For low density of scatterers or strong interactions the wave function extends over the whole interval. High density of scatterers and weak interaction, on the other hand, leads to localization of the wave function in a fragmented subset of the unit interval.
© EDP Sciences, Springer-Verlag, 2013
