Attractive gases in 1D: thermal phase transition
An international collaboration led by Dr. Christoph Weiss, Durham University, UK, currently investigates the influence of temperature on one-dimensional (1D) attractive gases [1-3]. Trains or narrow rivers are examples of effectively one-dimensional motion in our three-dimensional world. In winter rivers are less likely to freeze than, say, lakes. Scientists had expected that this also is true for quantum systems. Surprisingly, attractively interacting Bose gases in a very elongated, thus effectively one-dimensional "tube", display a low-temperature behaviour similar to water turning into ice .
Processes like water freezing / ice melting are called "phase transitions". For thermally isolated ultracold attractive Bose gases, the low-temperature phase (a large bright soliton) and the high-temperature phase (free gas) contrary to previous predictions [1,5] co-exist . As the relative distance between attractive bosons cannot become large, this phase transition does not violate the Mermin-Wagner theorem . Dr. Weiss says "surprisingly, the new findings  also differ considerably from the assumption that all particles form the bright soliton." The assumption that all particles form the bright soliton is made by the mean-field theory (Gross-Piteavskii equation). State-of-the-art experiments with bright solitons in Bose-Einstein condensates often are modelled with mean-field theory. The quasi-1D geometry prevents attractive Bose-Einstein condensates from collapsing.
 C. Weiss, "Finite-temperature phase transition in a homogeneous one-dimensional gas of attractive bosons", https://arxiv.org/abs/1610.
 C. Weiss, S. A. Gardiner and B. Gertjerenken "Temperatures are not useful to characterise bright-soliton experiments for ultra-cold atoms", https://arxiv.org/abs/1610.
 C. Weiss, S. A. Gardiner, J. Tempere and B. Gertjerenken, manuscript in preparation.
 Mermin-Wagner Theorem http://www.scholarpedia.org/
 C. Herzog, M. Olshanii, Y. Castin, Comptes Rendus Physique 15 (2014) 285, https://arxiv.org/abs/1311.