Calculation of the critical temperature of a dilute Bose gas in the Bogoliubov approximation Journal Article

Author(s): Napiórkowski, Marcin; Reuvers, Robin; Solovej, Jan P
Article Title: Calculation of the critical temperature of a dilute Bose gas in the Bogoliubov approximation
Affiliation IST Austria
Abstract: Following an earlier calculation in 3D, we calculate the 2D critical temperature of a dilute, translation-invariant Bose gas using a variational formulation of the Bogoliubov approximation introduced by Critchley and Solomon in 1976. This provides the first analytical calculation of the Kosterlitz-Thouless transition temperature that includes the constant in the logarithm.
Journal Title: EPL
Volume: 121
Issue 1
ISSN: 02955075
Publisher: IOP Publishing Ltd.  
Date Published: 2018-01-01
Start Page: Article number: 10007
DOI: 10.1209/0295-5075/121/10007
Notes: To improve the model one would have to extend the class of trial states, which is both very interesting and very challenging. Another compelling direction for future research is to ask what role superfluidity plays in this model, and what we can learn from it. ∗∗∗ We thank Robert Seiringer and Daniel Ueltschi for bringing the issue of the change in critical temperature to our attention. We also thank the Erwin Schrödinger Institute (all authors) and the Department of Mathematics, University of Copenhagen (MN) for the hospitality during the period this work was carried out. We gratefully acknowledge the financial support by the European Unions Seventh Framework Programme under the ERC Grant Agreement Nos. 321029 (JPS and RR) and 337603 (RR) as well as support by the VIL-LUM FONDEN via the QMATH Centre of Excellence (Grant No. 10059) (JPS and RR), by the National Science Center (NCN) under grant No. 2016/21/D/ST1/02430 and the Austrian Science Fund (FWF) through project No. P 27533-N27 (MN).
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