Transition temperature of the weakly interacting Bose gas: perturbative solution of the crossover equations in the canonical ensemble
- We compute the shift of the critical temperature Tc with respect to the ideal case for a weakly interacting uniform Bose gas. We work in the framework of the canonical ensemble, extending the criterion of condensation provided by the canonical particle counting statistics for the zero-momentum state of the uniform ideal gas. The perturbative solution of the crossover equation to lowest order in power of the scattering length yields (Tc - Tc0)/Tc0=-0,93ap 1/3, where Tc0 is the transition temperature of the corresponding ideal Bose gas , a is the scattering length, and p is the particle number density. This is at vaiance with the standard grand canonical prediction of a null shift of the critical temperature in the lowest perturbative order. The non-equevalence of statistical ensemble for the ideal Bose gas is thus confirm (at the lowestperturbative level) also in the presence of interactions.
Author details: | Martin WilkensORCiD, Fabrizio Illuminati, Meret Krämer |
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Publication type: | Article |
Language: | English |
Year of first publication: | 2000 |
Publication year: | 2000 |
Release date: | 2017/03/24 |
Source: | Journal of Physics / B. - 33 (2000), S. 779 - 786 |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie |
Institution name at the time of the publication: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik |