https://doi.org/10.1007/BF01325463
Two-dimensional dilute Bose gas in the normal phase
Dipartimento di Matematica e Fisica, Sezione INFM,
Università di Camerino, 62032 Camerino, Italy
Corresponding author: a pieri@campus.unicam.it
Received:
3
March
2001
Revised:
9
April
2001
Published online: 15 July 2001
We consider a two-dimensional dilute Bose gas above its superfluid transition temperature. We show that the t-matrix approximation corresponds to the leading set of diagrams in the dilute limit, provided the temperature is sufficiently larger than the superfluid transition temperature. Within this approximation, we give an explicit expression for the wave-vector and frequency dependence of the self-energy, and calculate the corrections to the chemical potential and the effective mass arising from the interaction. We also argue that the breakdown of diagrammatic classification scheme for the dilute Bose gas, which occurs upon lowering the temperature, provides a criterion to estimate an upper bound for the superfluid critical temperature. The upper bound to the critical temperature identified by this criterion turns out to coincide with earlier results for the critical temperature obtained by Popov and by Fisher and Hohenberg using different methods. Extension of this procedure to the three-dimensional case gives good agreement with recent Monte Carlo data.
PACS: 05.30.Jp – Boson systems / 05.70.Fh – Phase transitions: general studies / 03.75.Fi – Phase coherent atomic ensembles; quantum condensation phenomena
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2001