Instability in a two-dimensional dilute interacting Bose system

The formalism of Ursell operators provides a self-consistent integral equat ion for the one-particle reduced operator. In three dimensions this techniq ue yields values of the shift in the Bose-Einstein condensation (BEC) trans ition temperature, as a function of the scattering length, that are in good agreement with those of Green's function and quantum Monte Carlo methods. We have applied the same equations to a uniform two-dimensional system and find that, as we alter the chemical potential, an instability develops so t hat the self-consistent equations no longer have a solution. This instabili ty, which seems to indicate that interactions restore a transition, occurs at a non-zero value of an effective chemical potential. The non-linear equa tions are limited to temperatures greater than or equal to Tc, so that they do not indicate the nature of the new stable state: belt we speculate conc erning whether it is a Kosterlitz-Thouless state or a "smeared" BEC, which might avoid any violation of the Hohenberg theorem, as described in an acco mpanying paper.