The thermodynamic properties and finite-size scaling of weakly interacting Bose gases with a finite number of particles confined in a cubic box of volume ${L}^{3}$ with periodic boundary conditions are investigated theoretically based on an exact recursion relation for the canonical-ensemble partition function. In a similar manner to the case of an ideal Bose gas, the recursive scheme of the interacting finite system at any temperatures is established in the framework of the Bogoliubov theory. The temperature dependence of the condensate fraction and specific heat with different particles and interactions is obtained numerically. By defining two different transition temperatures of the finite systems, the effect of interactions on the transition temperatures yields the different and nonmonotonous behaviors. The finite-size scaling condensate fraction at the transition temperature for the systems is also discussed. It is shown that the calculated finite-size scaling is universally independent on the various system sizes and transition temperatures.The thermodynamic properties and finite-size scaling of weakly interacting Bose gases with a finite number of particles confined in a cubic box of volume ${L}^{3}$ with periodic boundary conditions are investigated theoretically based on an exact recursion relation for the canonical-ensemble partition function. In a similar manner to the case of an ideal Bose gas, the recursive scheme of the interacting finite system at any temperatures is established in the framework of the Bogoliubov theory. The temperature dependence of the condensate fraction and specific heat with different particles and interactions is obtained numerically. By defining two different transition temperatures of the finite systems, the effect of interactions on the transition temperatures yields the different and nonmonotonous behaviors. The finite-size scaling condensate fraction at the transition temperature for the systems is also discussed. It is shown that the calculated finite-size scaling is universally independent on the various system sizes and transition temperatures.

Physical Review AMar 5, 200933 citations

Finite-size scaling and the role of the thermodynamic ensemble in the transition temperature of a dilute Bose gas

Erich J. Mueller, Gordon Baym, Markus Holzmann

We study the Bose-Einstein condensation phase transition in a weakly interacting gas through a perturbative analysis of finite systems. In both the grand canonical and the canonical ensembles, perturbation theory suffers from infrared divergences and cannot directly determine the transition temperature in the thermodynamic limit. However, in conjunction with finite-size scaling, perturbation theory provides a powerful calculation tool. Here we use this combination of perturbation theory and scaling to estimate a shift in the transition temperature in the canonical ensemble consistent with grand canonical calculations.We study the Bose-Einstein condensation phase transition in a weakly interacting gas through a perturbative analysis of finite systems. In both the grand canonical and the canonical ensembles, perturbation theory suffers from infrared divergences and cannot directly determine the transition temperature in the thermodynamic limit. However, in conjunction with finite-size scaling, perturbation theory provides a powerful calculation tool. Here we use this combination of perturbation theory and scaling to estimate a shift in the transition temperature in the canonical ensemble consistent with grand canonical calculations.

arXiv:cond-mat/0105359Journal of Physics B Atomic Molecular and Optical PhysicsNov 23, 200114 citations

Canonical and Grand–Canonical Ensembles for Trapped Bose Gases

Abel Camacho, Alfredo Macı́as, A. Camacho-Galván

WORLD SCIENTIFIC eBooksMay 1, 20100 citations

Scaling in the ideal Bose gas

Carol K. Hall

Journal of Statistical PhysicsAug 1, 197517 citations

Microcanonical finite-size scaling of an ideal Bose gas in a box

Honghui Wang, Jizhou He, Jianhui Wang

The European Physical Journal DJan 1, 20170 citations

The thermodynamic properties and finite-size scaling of weakly interacting Bose gases with a finite number of particles confined in a cubic box of volume

{L}^{3}

with periodic boundary conditions are investigated theoretically based on an exact recursion relation for the canonical-ensemble partition function. In a similar manner to the case of an ideal Bose gas, the recursive scheme of the interacting finite system at any temperatures is established in the framework of the Bogoliubov theory. The temperature dependence of the condensate fraction and specific heat with different particles and interactions is obtained numerically. By defining two different transition temperatures of the finite systems, the effect of interactions on the transition temperatures yields the different and nonmonotonous behaviors. The finite-size scaling condensate fraction at the transition temperature for the systems is also discussed. It is shown that the calculated finite-size scaling is universally independent on the various system sizes and transition temperatures.