Interaction-induced crossover versus finite-size condensation in a   weakly interacting trapped one-dimensional Bose gas
  We discuss the transition from a fully decoherent to a (quasi-)condensate regime in a harmonically trapped weakly interacting 1D Bose gas. By using analytic approaches and verifying them against exact numerical solutions, we find a characteristic crossover temperature and crossover atom number that depend on the interaction strength and the trap frequency. We then identify the conditions for observing either an interaction-induced crossover scenario or else a finite-size Bose-Einstein condensation phenomenon characteristic of an \textit{ideal} trapped 1D gas. 
Isabelle Bouchoule (LCFIO), Karen V. Kheruntsyan (ARC Centre of   Excellence for Quantum-Atom Optics), Gora Shlyapnikov (LPTMS)