$1/N$-expansion for the critical temperature of the Bose gas

Abstract

We revised the large-$N$ expansion for a three-dimensional Bose system with short-range repulsion in normal phase. Particularly, for the model potential that is characterised only by the $s$-wave scattering length $a$ the full numerical calculations of the critical temperature in the $1/N$-approximation as a function of the gas parameter $a{n}^{1/3}$ are performed. Additionally to the well-known result in the dilute limit we estimated analytically the leading-order strong-coupling behavior of the Bose-Einstein condensation transition temperature. It is shown that the critical temperature shift of the non-ideal Bose gas grows at small $a{n}^{1/3}$, reaches some maximal value and then falls down becoming negative.

6 pages, 3 figures

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Cited by in corpus (4)

• Polaron in the dilute critical Bose condensate
• Large-$N$ expansion for condensation and stability of Bose-Bose mixtures at finite temperatures
• Large-$N$ properties of a non-ideal Bose gas
• Condensation and superfluidity of $SU(N)$ Bose gas