SUPERFLUID PHASE TRANSITIONS IN ONE AND 2 DIMENSIONS

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. © 1968 The American Physical Society.