Existence of Bose-Einstein condensation in one and two dimensions

H. Perez Rojas

Piotr Stachura, Wiesław Pusz, Jacek Wojtkiewicz

We apply the Bogoliubov inequality to the Bose–Hubbard model to rule out the possibility of Bose–Einstein condensation. The result holds in one and two dimensions for any filling at any nonzero temperature. This result can be considered as complementary to the analogous, classical result known for interacting bosons in a continuum.

Y. Imry, David J. Bergman, Leon Gunther

Daomin Cao, Jinchun He, Haoyuan Xu +1 more

In this paper, we prove the existence of the positive ground state solution to fractional spin-1 Bose-Einstein condensation(BEC) in one dimension.

Allan Widom

A recently proved theorem of statistical physics states that a one- or two-dimensional Bose liquid in homogeneous thermodynamic equilibrium cannot undergo Bose-Einstein condensation. The theorem does not apply to inhomogeneous liquids. This is shown by considering the ideal Bose liquid (i) in the presence of a gravitational field and (ii) in rotational motion. The existence of well-defined one- and two-dimensional phase transitions with Bose-Einstein condensation is proved by these explicit examples.

Alain Aspect