2012/07/30 by Robert Seiringer, R. Seiringer, Jakob Yngvason +3
Mathematics · Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Quantum many-body systems #Spectral Theory in Mathematical Physics #cond-mat.quant-gas #math-ph #math.MP #msc:81V70 #msc:82D50
paper · pdf · doi:10.1088/1742-5468/2012/11/p11007
published as J. Stat. Mech. P11007 (2012)
arxiv created 2012/07/30 · openalex publication_date 2012/11/09 · arxiv updated 2013/01/25 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30
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 in the Gross–Pitaevskii regime. We prove that Bose–Einstein condensation survives even a strong random potential with a high density of scatterers. The character of the wavefunction 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 and strong interactions the wavefunction extends over the whole interval. A high density of scatterers and weak interactions, on the other hand, lead to localization of the wavefunction in a fragmented subset of the interval.