Beyond the dilute Bose gas

Subir Sachdev A

Jens O. Andersen

We consider the nonrelativistic interacting Bose gas at zero and finite temperature. Using the 1/N-expansion, we derive expressions for the free energy density and the number density to next-to-leading order in 1/N. Outside the critical region and at weak coupling, our calculations reduce to the well-known mean-field results for the dilute Bose gas. We also rederive the nonperturbative critical density for Bose condensation which was first calculated by Baym, Blaizot, Holzmann, Lalöe, and Vautherin.

Markus Holzmann, Gordon Baym, Jean-Paul Blaizot +1 more

We show that the shift in the transition temperature of the dilute homogeneous Bose gas is nonanalytic in the scattering amplitude a. The first correction beyond the positive linear shift in a is negative and of order a(2)lna. This nonuniversal nonanalytic structure indicates how the discrepancies between numerical calculations at finite a can be reconciled with calculations of the limit a-->0, since the linearity is apparent only for anomalously small a.

Victor Nikolaevich Popov