The transition temperature of the dilute interacting Bose gas

Gordon Baym (1, 2, 3) , Jean-Paul Blaizot (2) , Markus Holzmann (1, 4) , Dominique Vautherin (5) , Franck Laloë (1)

1 LKB (Lhomond) - Laboratoire Kastler Brossel
2 SPhT - Service de Physique Théorique
3 UIUC - Physics Department
4 LPS - Laboratoire de Physique Statistique de l'ENS
5 LPNHE - Laboratoire de Physique Nucléaire et de Hautes Énergies

We show that the critical temperature of a uniform dilute Bose gas increases linearly with the s-wave scattering length describing the repulsion between the particles. Because of infrared divergences, the magnitude of the shift cannot be obtained from perturbation theory, even in the weak coupling regime; rather, it is proportional to the size of the critical region in momentum space. By means of a self-consistent calculation of the quasiparticle spectrum at low momenta at the transition, we find an estimate of the effect in reasonable agreement with numerical simulations.

Mots clés: critical temperature; Bose Einstein; dilute quantum gas

Domaines: Mécanique statistique [cond-mat.stat-mech]

Gordon Baym, Jean-Paul Blaizot, Markus Holzmann, Dominique Vautherin, Franck Laloë. The transition temperature of the dilute interacting Bose gas. Physical Review Letters, 1999, 83, pp.1703-1706. ⟨10.1103/PhysRevLett.83.1703⟩. ⟨hal-00001411⟩